数学。怎样用十字相乘法解？ 谁能讲讲数学里的十字相乘法
\u6570\u5b66\u5341\u5b57\u76f8\u4e58\u7684\u7528\u6cd5\u3002\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u89e3\u4e00\u5143\uff1d\u6b21\u65b9\u7a0b
1\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u65b9\u6cd5\uff1a\u5341\u5b57\u5de6\u8fb9\u76f8\u4e58\u7b49\u4e8e\u4e8c\u6b21\u9879\u7cfb\u6570\uff0c\u53f3\u8fb9\u76f8\u4e58\u7b49\u4e8e\u5e38\u6570\u9879\uff0c\u4ea4\u53c9\u76f8\u4e58\u518d\u76f8\u52a0\u7b49\u4e8e\u4e00\u6b21\u9879\u7cfb\u6570\u3002
2\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u7528\u5904\uff1a\uff081\uff09\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u5206\u89e3\u56e0\u5f0f\u3002\uff082\uff09\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u3002
3\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u4f18\u70b9\uff1a\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u9898\u7684\u901f\u5ea6\u6bd4\u8f83\u5feb\uff0c\u80fd\u591f\u8282\u7ea6\u65f6\u95f4\uff0c\u800c\u4e14\u8fd0\u7528\u7b97\u91cf\u4e0d\u5927\uff0c\u4e0d\u5bb9\u6613\u51fa\u9519\u3002
4\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u7f3a\u9677\uff1a1\u3001\u6709\u4e9b\u9898\u76ee\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u6bd4\u8f83\u7b80\u5355\uff0c\u4f46\u5e76\u4e0d\u662f\u6bcf\u4e00\u9053\u9898\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u90fd\u7b80\u5355\u30022\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u53ea\u9002\u7528\u4e8e\u4e8c\u6b21\u4e09\u9879\u5f0f\u7c7b\u578b\u7684\u9898\u76ee\u30023\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u6bd4\u8f83\u96be\u5b66\u3002
5\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u89e3\u9898\u5b9e\u4f8b\uff1a
1)\u3001 \u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u89e3\u4e00\u4e9b\u7b80\u5355\u5e38\u89c1\u7684\u9898\u76ee
\u4f8b1\u628am²+4m-12\u5206\u89e3\u56e0\u5f0f (²\u8868\u793a\u5e73\u65b9,\u4e0b\u540c)
\u5206\u6790\uff1a\u672c\u9898\u4e2d\u5e38\u6570\u9879-12\u53ef\u4ee5\u5206\u4e3a-1\u00d712\uff0c-2\u00d76\uff0c-3\u00d74\uff0c-4\u00d73\uff0c-6\u00d72\uff0c-12\u00d71\u5f53-12\u5206\u6210-2\u00d76\u65f6\uff0c\u624d\u7b26\u5408\u672c\u9898
\u89e3\uff1a\u56e0\u4e3a 1 -2
1 \u2573 6
\u6240\u4ee5m²+4m-12=\uff08m-2\uff09\uff08m+6\uff09
\u4f8b2\u628a5x²+6x-8\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u672c\u9898\u4e2d\u76845\u53ef\u5206\u4e3a1\u00d75,-8\u53ef\u5206\u4e3a-1\u00d78\uff0c-2\u00d74\uff0c-4\u00d72\uff0c-8\u00d71\u3002\u5f53\u4e8c\u6b21\u9879\u7cfb\u6570\u5206\u4e3a1\u00d75\uff0c\u5e38\u6570\u9879\u5206\u4e3a-4\u00d72\u65f6\uff0c\u624d\u7b26\u5408\u672c\u9898
\u89e3\uff1a \u56e0\u4e3a 1 2
5 \u2573 -4
\u6240\u4ee55x²+6x-8=\uff08x+2\uff09\uff085x-4\uff09
\u4f8b3\u89e3\u65b9\u7a0bx²-8x+15=0
\u5206\u6790\uff1a\u628ax²-8x+15\u770b\u6210\u5173\u4e8ex\u7684\u4e00\u4e2a\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u521915\u53ef\u5206\u62101\u00d715\uff0c3\u00d75\u3002
\u89e3\uff1a \u56e0\u4e3a 1 -3
1 \u2573 -5
\u6240\u4ee5\u539f\u65b9\u7a0b\u53ef\u53d8\u5f62\uff08x-3\uff09\uff08x-5\uff09=0
\u6240\u4ee5x1=3 x2=5
\u4f8b4\u3001\u89e3\u65b9\u7a0b 6x²-5x-25=0
\u5206\u6790\uff1a\u628a6x²-5x-25\u770b\u6210\u4e00\u4e2a\u5173\u4e8ex\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u52196\u53ef\u4ee5\u5206\u4e3a1\u00d76\uff0c2\u00d73\uff0c-25\u53ef\u4ee5\u5206\u6210-1\u00d725\uff0c-5\u00d75\uff0c-25\u00d71\u3002
\u89e3\uff1a \u56e0\u4e3a 2 -5
3 \u2573 5
\u6240\u4ee5 \u539f\u65b9\u7a0b\u53ef\u53d8\u5f62\u6210\uff082x-5\uff09\uff083x+5\uff09=0
\u6240\u4ee5 x1=5/2 x2=-5/3
2)\u3001\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u89e3\u4e00\u4e9b\u6bd4\u8f83\u96be\u7684\u9898\u76ee
\u4f8b5\u628a14x²-67xy+18y²\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u628a14x²-67xy+18y²\u770b\u6210\u662f\u4e00\u4e2a\u5173\u4e8ex\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f,\u521914\u53ef\u5206\u4e3a1\u00d714,2\u00d77, 18y²\u53ef\u5206\u4e3ay.18y , 2y.9y , 3y.6y
\u89e3: \u56e0\u4e3a 2 -9y
7 \u2573 -2y
\u6240\u4ee5 14x²-67xy+18y²= (2x-9y)(7x-2y)
\u4f8b6 \u628a10x²-27xy-28y²-x+25y-3\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u5728\u672c\u9898\u4e2d\uff0c\u8981\u628a\u8fd9\u4e2a\u591a\u9879\u5f0f\u6574\u7406\u6210\u4e8c\u6b21\u4e09\u9879\u5f0f\u7684\u5f62\u5f0f
\u89e3\u6cd5\u4e00\u300110x²-27xy-28y²-x+25y-3
=10x²-\uff0827y+1\uff09x -\uff0828y²-25y+3\uff09 4y -3
7y \u2573 -1
=10x²-\uff0827y+1\uff09x -\uff084y-3\uff09\uff087y -1\uff09
=[2x -\uff087y -1\uff09][5x +\uff084y -3\uff09] 2 -\uff087y \u2013 1\uff09
5 \u2573 4y - 3
=\uff082x -7y +1\uff09\uff085x +4y -3\uff09
\u8bf4\u660e\uff1a\u5728\u672c\u9898\u4e2d\u5148\u628a28y²-25y+3\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u4e3a\uff084y-3\uff09\uff087y -1\uff09\uff0c\u518d\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u628a10x²-\uff0827y+1\uff09x -\uff084y-3\uff09\uff087y -1\uff09\u5206\u89e3\u4e3a[2x -\uff087y -1\uff09][5x +\uff084y -3\uff09]
\u89e3\u6cd5\u4e8c\u300110x²-27xy-28y²-x+25y-3
=\uff082x -7y\uff09\uff085x +4y\uff09-\uff08x -25y\uff09- 3 2 -7y
=[\uff082x -7y\uff09+1] [\uff085x -4y\uff09-3] 5 \u2573 4y
=\uff082x -7y+1\uff09\uff085x -4y -3\uff09 2 x -7y 1
5 x - 4y \u2573 -3
\u8bf4\u660e:\u5728\u672c\u9898\u4e2d\u5148\u628a10x²-27xy-28y²\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u4e3a\uff082x -7y\uff09\uff085x +4y\uff09,\u518d\u628a\uff082x -7y\uff09\uff085x +4y\uff09-\uff08x -25y\uff09- 3\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u4e3a[\uff082x -7y\uff09+1] [\uff085x -4y\uff09-3].
\u4f8b7\uff1a\u89e3\u5173\u4e8ex\u65b9\u7a0b\uff1ax²- 3ax + 2a²\u2013ab -b²=0
\u5206\u6790\uff1a2a²\u2013ab-b²\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3
\u89e3\uff1ax²- 3ax + 2a²\u2013ab -b²=0
x²- 3ax +\uff082a²\u2013ab - b²\uff09=0
x²- 3ax +\uff082a+b\uff09\uff08a-b\uff09=0 1 -b
2 \u2573 +b
[x-\uff082a+b\uff09][ x-\uff08a-b\uff09]=0 1 -\uff082a+b\uff09
1 \u2573 -\uff08a-b\uff09
\u6240\u4ee5 x1=2a+b x2=a-b
\u2474\u63d0\u516c\u56e0\u5f0f\u6cd5
\u2460\u516c\u56e0\u5f0f\uff1a\u5404\u9879\u90fd\u542b\u6709\u7684\u516c\u5171\u7684\u56e0\u5f0f\u53eb\u505a\u8fd9\u4e2a\u591a\u9879\u5f0f\u5404\u9879\u7684\u516c\u56e0\u5f0f\u3002
\u2461\u63d0\u516c\u56e0\u5f0f\u6cd5\uff1a\u4e00\u822c\u5730\uff0c\u5982\u679c\u591a\u9879\u5f0f\u7684\u5404\u9879\u6709\u516c\u56e0\u5f0f\uff0c\u53ef\u4ee5\u628a\u8fd9\u4e2a\u516c\u56e0\u5f0f\u63d0\u5230\u62ec\u53f7\u5916\u9762\uff0c\u5c06\u591a\u9879\u5f0f\u5199\u6210\u56e0\u5f0f\u4e58\u79ef\u7684\u5f62\u5f0f\uff0c\u8fd9\u79cd\u5206\u89e3\u56e0\u5f0f\u7684\u65b9\u6cd5\u53eb\u505a\u63d0\u516c\u56e0\u5f0f\u6cd5.\u3002
am\uff0bbm\uff0bcm\uff1dm\uff08a+b+c\uff09
\u2462\u5177\u4f53\u65b9\u6cd5\uff1a\u5f53\u5404\u9879\u7cfb\u6570\u90fd\u662f\u6574\u6570\u65f6\uff0c\u516c\u56e0\u5f0f\u7684\u7cfb\u6570\u5e94\u53d6\u5404\u9879\u7cfb\u6570\u7684\u6700\u5927\u516c\u7ea6\u6570\uff1b\u5b57\u6bcd\u53d6\u5404\u9879\u7684\u76f8\u540c\u7684\u5b57\u6bcd\uff0c\u800c\u4e14\u5404\u5b57\u6bcd\u7684\u6307\u6570\u53d6\u6b21\u6570\u6700\u4f4e\u7684. \u5982\u679c\u591a\u9879\u5f0f\u7684\u7b2c\u4e00\u9879\u662f\u8d1f\u7684\uff0c\u4e00\u822c\u8981\u63d0\u51fa\u201c\uff0d\u201d\u53f7\uff0c\u4f7f\u62ec\u53f7\u5185\u7684\u7b2c\u4e00\u9879\u7684\u7cfb\u6570\u662f\u6b63\u7684.
\u2475\u8fd0\u7528\u516c\u5f0f\u6cd5
\u2460\u5e73\u65b9\u5dee\u516c\u5f0f\uff1a. a^2\uff0db^2\uff1d(a\uff0bb)(a\uff0db)
\u2461\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\uff1a a^2\u00b12ab\uff0bb^2\uff1d(a\u00b1b)^2
\u203b\u80fd\u8fd0\u7528\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u5206\u89e3\u56e0\u5f0f\u7684\u591a\u9879\u5f0f\u5fc5\u987b\u662f\u4e09\u9879\u5f0f,\u5176\u4e2d\u6709\u4e24\u9879\u80fd\u5199\u6210\u4e24\u4e2a\u6570(\u6216\u5f0f)\u7684\u5e73\u65b9\u548c\u7684\u5f62\u5f0f\uff0c\u53e6\u4e00\u9879\u662f\u8fd9\u4e24\u4e2a\u6570(\u6216\u5f0f)\u7684\u79ef\u76842\u500d.
\u2462\u7acb\u65b9\u548c\u516c\u5f0f\uff1aa^3+b^3\uff1d (a+b)(a^2-ab+b^2).
\u7acb\u65b9\u5dee\u516c\u5f0f\uff1aa^3-b^3\uff1d (a-b)(a^2+ab+b^2).
\u2463\u5b8c\u5168\u7acb\u65b9\u516c\u5f0f\uff1a a^3\u00b13a^2b\uff0b3ab^2\u00b1b^3\uff1d(a\u00b1b)^3
\u2464a^n-b^n=(a-b)[a^(n-1)+a^(n-2)b+\u2026\u2026+b^(n-2)a+b^(n-1)]
a^m+b^m=(a+b)[a^(m-1)-a^(m-2)b+\u2026\u2026-b^(m-2)a+b^(m-1)](m\u4e3a\u5947\u6570)
\u2476\u5206\u7ec4\u5206\u89e3\u6cd5
\u5206\u7ec4\u5206\u89e3\u6cd5\uff1a\u628a\u4e00\u4e2a\u591a\u9879\u5f0f\u5206\u7ec4\u540e\uff0c\u518d\u8fdb\u884c\u5206\u89e3\u56e0\u5f0f\u7684\u65b9\u6cd5.
\u5206\u7ec4\u5206\u89e3\u6cd5\u5fc5\u987b\u6709\u660e\u786e\u76ee\u7684\uff0c\u5373\u5206\u7ec4\u540e\uff0c\u53ef\u4ee5\u76f4\u63a5\u63d0\u516c\u56e0\u5f0f\u6216\u8fd0\u7528\u516c\u5f0f.
\u2477\u62c6\u9879\u3001\u8865\u9879\u6cd5
\u62c6\u9879\u3001\u8865\u9879\u6cd5\uff1a\u628a\u591a\u9879\u5f0f\u7684\u67d0\u4e00\u9879\u62c6\u5f00\u6216\u586b\u8865\u4e0a\u4e92\u4e3a\u76f8\u53cd\u6570\u7684\u4e24\u9879\uff08\u6216\u51e0\u9879\uff09\uff0c\u4f7f\u539f\u5f0f\u9002\u5408\u4e8e\u63d0\u516c\u56e0\u5f0f\u6cd5\u3001\u8fd0\u7528\u516c\u5f0f\u6cd5\u6216\u5206\u7ec4\u5206\u89e3\u6cd5\u8fdb\u884c\u5206\u89e3\uff1b\u8981\u6ce8\u610f\uff0c\u5fc5\u987b\u5728\u4e0e\u539f\u591a\u9879\u5f0f\u76f8\u7b49\u7684\u539f\u5219\u8fdb\u884c\u53d8\u5f62.
\u2478\u5341\u5b57\u76f8\u4e58\u6cd5
\u2460x^2\uff0b\uff08p q\uff09x\uff0bpq\u578b\u7684\u5f0f\u5b50\u7684\u56e0\u5f0f\u5206\u89e3
\u8fd9\u7c7b\u4e8c\u6b21\u4e09\u9879\u5f0f\u7684\u7279\u70b9\u662f\uff1a\u4e8c\u6b21\u9879\u7684\u7cfb\u6570\u662f1\uff1b\u5e38\u6570\u9879\u662f\u4e24\u4e2a\u6570\u7684\u79ef\uff1b\u4e00\u6b21\u9879\u7cfb\u6570\u662f\u5e38\u6570\u9879\u7684\u4e24\u4e2a\u56e0\u6570\u7684\u548c.\u56e0\u6b64\uff0c\u53ef\u4ee5\u76f4\u63a5\u5c06\u67d0\u4e9b\u4e8c\u6b21\u9879\u7684\u7cfb\u6570\u662f1\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\uff1a x^2\uff0b\uff08p q\uff09x\uff0bpq\uff1d\uff08x\uff0bp\uff09\uff08x\uff0bq\uff09
\u2461kx^2\uff0bmx\uff0bn\u578b\u7684\u5f0f\u5b50\u7684\u56e0\u5f0f\u5206\u89e3
\u5982\u679c\u80fd\u591f\u5206\u89e3\u6210k\uff1dac\uff0cn\uff1dbd\uff0c\u4e14\u6709ad\uff0bbc\uff1dm \u65f6\uff0c\u90a3\u4e48
kx^2\uff0bmx\uff0bn\uff1d\uff08ax b\uff09\uff08cx d\uff09
a \-----/b ac\uff1dk bd\uff1dn
c /-----\d ad\uff0bbc\uff1dm
\u203b \u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u7684\u4e00\u822c\u6b65\u9aa4\uff1a
\u2460\u5982\u679c\u591a\u9879\u5f0f\u7684\u5404\u9879\u6709\u516c\u56e0\u5f0f\uff0c\u90a3\u4e48\u5148\u63d0\u516c\u56e0\u5f0f\uff1b
\u2461\u5982\u679c\u5404\u9879\u6ca1\u6709\u516c\u56e0\u5f0f\uff0c\u90a3\u4e48\u53ef\u5c1d\u8bd5\u8fd0\u7528\u516c\u5f0f\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u5206\u89e3\uff1b
\u2462\u5982\u679c\u7528\u4e0a\u8ff0\u65b9\u6cd5\u4e0d\u80fd\u5206\u89e3\uff0c\u90a3\u4e48\u53ef\u4ee5\u5c1d\u8bd5\u7528\u5206\u7ec4\u3001\u62c6\u9879\u3001\u8865\u9879\u6cd5\u6765\u5206\u89e3\uff1b
\u2463\u5206\u89e3\u56e0\u5f0f\uff0c\u5fc5\u987b\u8fdb\u884c\u5230\u6bcf\u4e00\u4e2a\u591a\u9879\u5f0f\u56e0\u5f0f\u90fd\u4e0d\u80fd\u518d\u5206\u89e3\u4e3a\u6b62\u3002
(6)\u5e94\u7528\u56e0\u5f0f\u5b9a\u7406\uff1a\u5982\u679cf\uff08a\uff09=0\uff0c\u5219f\uff08x\uff09\u5fc5\u542b\u6709\u56e0\u5f0f\uff08x-a\uff09\u3002\u5982f\uff08x\uff09=x^2+5x+6\uff0cf\uff08-2\uff09=0\uff0c\u5219\u53ef\u786e\u5b9a\uff08x+2\uff09\u662fx^2+5x+6\u7684\u4e00\u4e2a\u56e0\u5f0f\u3002
\u7ecf\u5178\u4f8b\u9898\uff1a
1.\u5206\u89e3\u56e0\u5f0f(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2
\u89e3\uff1a\u539f\u5f0f=(1+y)^2+2(1+y)x^2(1+y)+x^4(1-y)^2-2(1+y)x^2(1-y)-2x^2(1+y^2)
=[(1+y)+x^2(1-y)]^2-2(1+y)x^2(1-y)-2x^2(1+y^2)
=[(1+y)+x^2(1-y)]^2-(2x)^2
=[(1+y)+x^2(1-y)+2x]\u00b7[(1+y)+x^2(1-y)-2x]
=(x^2-x^2y+2x+y+1)(x^2-x^2y-2x+y+1)
=[(x+1)^2-y(x^2-1)][(x-1)^2-y(x^2-1)]
=(x+1)(x+1-xy+y)(x-1)(x-1-xy-y)
2.\u8bc1\u660e\uff1a\u5bf9\u4e8e\u4efb\u4f55\u6570x,y\uff0c\u4e0b\u5f0f\u7684\u503c\u90fd\u4e0d\u4f1a\u4e3a33
x^5+3x^4y-5x^3y^2+4xy^4+12y^5
\u89e3\uff1a\u539f\u5f0f=(x^5+3x^4y)-(5x^3y^2+15x^2y^3)+(4xy^4+12y^5)
=x^4(x+3y)-5x^2y^2(x+3y)+4y^4(x+3y)
=(x+3y)(x^4-5x^2y^2+4y^4)
=(x+3y)(x^2-4y^2)(x^2-y^2)
=(x+3y)(x+y)(x-y)(x+2y)(x-2y)
\u5f53y=0\u65f6\uff0c\u539f\u5f0f=x^5\u4e0d\u7b49\u4e8e33\uff1b\u5f53y\u4e0d\u7b49\u4e8e0\u65f6\uff0cx+3y,x+y,x-y,x+2y,x-2y\u4e92\u4e0d\u76f8\u540c\uff0c\u800c33\u4e0d\u80fd\u5206\u6210\u56db\u4e2a\u4ee5\u4e0a\u4e0d\u540c\u56e0\u6570\u7684\u79ef\uff0c\u6240\u4ee5\u539f\u547d\u9898\u6210\u7acb
\u56e0\u5f0f\u5206\u89e3\u7684\u5341\u4e8c\u79cd\u65b9\u6cd5
\u628a\u4e00\u4e2a\u591a\u9879\u5f0f\u5316\u6210\u51e0\u4e2a\u6574\u5f0f\u7684\u79ef\u7684\u5f62\u5f0f\uff0c\u8fd9\u79cd\u53d8\u5f62\u53eb\u505a\u628a\u8fd9\u4e2a\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u3002\u56e0\u5f0f\u5206\u89e3\u7684\u65b9\u6cd5\u591a\u79cd\u591a\u6837\uff0c\u73b0\u603b\u7ed3\u5982\u4e0b\uff1a
1\u3001 \u63d0\u516c\u56e0\u6cd5
\u5982\u679c\u4e00\u4e2a\u591a\u9879\u5f0f\u7684\u5404\u9879\u90fd\u542b\u6709\u516c\u56e0\u5f0f\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u628a\u8fd9\u4e2a\u516c\u56e0\u5f0f\u63d0\u51fa\u6765\uff0c\u4ece\u800c\u5c06\u591a\u9879\u5f0f\u5316\u6210\u4e24\u4e2a\u56e0\u5f0f\u4e58\u79ef\u7684\u5f62\u5f0f\u3002
\u4f8b1\u3001 \u5206\u89e3\u56e0\u5f0fx^3 -2x^2 -x(2003\u6dee\u5b89\u5e02\u4e2d\u8003\u9898)
x^3 -2x^2 -x=x(x^2 -2x-1)
2\u3001 \u5e94\u7528\u516c\u5f0f\u6cd5
\u7531\u4e8e\u5206\u89e3\u56e0\u5f0f\u4e0e\u6574\u5f0f\u4e58\u6cd5\u6709\u7740\u4e92\u9006\u7684\u5173\u7cfb\uff0c\u5982\u679c\u628a\u4e58\u6cd5\u516c\u5f0f\u53cd\u8fc7\u6765\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u7528\u6765\u628a\u67d0\u4e9b\u591a\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\u3002
\u4f8b2\u3001\u5206\u89e3\u56e0\u5f0fa^2 +4ab+4b^2 (2003\u5357\u901a\u5e02\u4e2d\u8003\u9898)
\u89e3\uff1aa^2 +4ab+4b^2 =\uff08a+2b\uff09
3\u3001 \u5206\u7ec4\u5206\u89e3\u6cd5
\u8981\u628a\u591a\u9879\u5f0fam+an+bm+bn\u5206\u89e3\u56e0\u5f0f\uff0c\u53ef\u4ee5\u5148\u628a\u5b83\u524d\u4e24\u9879\u5206\u6210\u4e00\u7ec4\uff0c\u5e76\u63d0\u51fa\u516c\u56e0\u5f0fa\uff0c\u628a\u5b83\u540e\u4e24\u9879\u5206\u6210\u4e00\u7ec4\uff0c\u5e76\u63d0\u51fa\u516c\u56e0\u5f0fb\uff0c\u4ece\u800c\u5f97\u5230a(m+n)+b(m+n),\u53c8\u53ef\u4ee5\u63d0\u51fa\u516c\u56e0\u5f0fm+n\uff0c\u4ece\u800c\u5f97\u5230(a+b)(m+n)
\u4f8b3\u3001\u5206\u89e3\u56e0\u5f0fm^2 +5n-mn-5m
\u89e3\uff1am^2+5n-mn-5m= m^2-5m -mn+5n
= (m^2 -5m )+(-mn+5n)
=m(m-5)-n(m-5)
=(m-5)(m-n)
4\u3001 \u5341\u5b57\u76f8\u4e58\u6cd5
\u5bf9\u4e8emx^2 +px+q\u5f62\u5f0f\u7684\u591a\u9879\u5f0f\uff0c\u5982\u679ca\u00d7b=m,c\u00d7d=q\u4e14ac+bd=p\uff0c\u5219\u591a\u9879\u5f0f\u53ef\u56e0\u5f0f\u5206\u89e3\u4e3a(ax+d)(bx+c)
\u4f8b4\u3001\u5206\u89e3\u56e0\u5f0f7x^2 -19x-6
\u5206\u6790\uff1a
1 -3
7 2
2-21=-19
\u89e3\uff1a7x^2 -19x-6=\uff087x+2\uff09(x-3)
5\u3001\u914d\u65b9\u6cd5
\u5bf9\u4e8e\u90a3\u4e9b\u4e0d\u80fd\u5229\u7528\u516c\u5f0f\u6cd5\u7684\u591a\u9879\u5f0f\uff0c\u6709\u7684\u53ef\u4ee5\u5229\u7528\u5c06\u5176\u914d\u6210\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u7136\u540e\u518d\u5229\u7528\u5e73\u65b9\u5dee\u516c\u5f0f\uff0c\u5c31\u80fd\u5c06\u5176\u56e0\u5f0f\u5206\u89e3\u3002
\u4f8b5\u3001\u5206\u89e3\u56e0\u5f0fx^2 +3x-40
\u89e3x^2 +3x-40
=x^2+3x+2.25-42.25
=(x+1.5)^2-(6.5)^2
=(x+8)(x-5)
6\u3001\u62c6\u3001\u6dfb\u9879\u6cd5
\u53ef\u4ee5\u628a\u591a\u9879\u5f0f\u62c6\u6210\u82e5\u5e72\u90e8\u5206\uff0c\u518d\u7528\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002
\u4f8b6\u3001\u5206\u89e3\u56e0\u5f0fbc(b+c)+ca(c-a)-ab(a+b)
\u89e3\uff1abc(b+c)+ca(c-a)-ab(a+b)=bc(c-a+a+b)+ca(c-a)-ab(a+b)
=bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b)
=c(c-a)(b+a)+b(a+b)(c-a)
=(c+b)(c-a)(a+b)
7\u3001 \u6362\u5143\u6cd5
\u6709\u65f6\u5728\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u53ef\u4ee5\u9009\u62e9\u591a\u9879\u5f0f\u4e2d\u7684\u76f8\u540c\u7684\u90e8\u5206\u6362\u6210\u53e6\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u7136\u540e\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u6700\u540e\u518d\u8f6c\u6362\u56de\u6765\u3002
\u4f8b7\u3001\u5206\u89e3\u56e0\u5f0f2x^4 -x^3 -6x^2 -x+2
8\u3001 \u6c42\u6839\u6cd5
\u4ee4\u591a\u9879\u5f0ff(x)=0,\u6c42\u51fa\u5176\u6839\u4e3ax1 ,x2 ,x3 ,\u2026\u2026xn ,\u5219\u591a\u9879\u5f0f\u53ef\u56e0\u5f0f\u5206\u89e3\u4e3af(x)=(x-x1 )(x-x2 )(x-x3 )\u2026\u2026(x-xn )
\u4f8b8\u3001\u5206\u89e3\u56e0\u5f0f2x^4 +7x^3 -2x^2 -13x+6
\u89e3\uff1a\u4ee4f(x)=2x^4 +7x^3 -2x^2 -13x+6=0
\u901a\u8fc7\u7efc\u5408\u9664\u6cd5\u53ef\u77e5\uff0cf(x)=0\u6839\u4e3a1/2 \uff0c-3\uff0c-2\uff0c1
\u52192x^4 +7x^3 -2x^2 -13x+6=(2x-1)(x+3)(x+2)(x-1)
9\u3001 \u56fe\u50cf\u6cd5
\u4ee4y=f(x)\uff0c\u505a\u51fa\u51fd\u6570y=f(x)\u7684\u56fe\u50cf\uff0c\u627e\u5230\u51fd\u6570\u56fe\u50cf\u4e0eX\u8f74\u7684\u4ea4\u70b9x1 ,x2 ,x3 ,\u2026\u2026xn \uff0c\u5219\u591a\u9879\u5f0f\u53ef\u56e0\u5f0f\u5206\u89e3\u4e3af(x)= f(x)=(x-x1 )(x-x2 )(x-x3 )\u2026\u2026(x-xn )
\u4f8b9\u3001\u56e0\u5f0f\u5206\u89e3x^3 +2x^2 -5x-6
\u89e3\uff1a\u4ee4y= x^3 +2x^2 -5x-6
\u4f5c\u51fa\u5176\u56fe\u50cf\uff0c\u4e0ex\u8f74\u4ea4\u70b9\u4e3a-3\uff0c-1\uff0c2
\u5219x^3 +2x^2 -5x-6=(x+1)(x+3)(x-2)
10\u3001 \u4e3b\u5143\u6cd5
\u5148\u9009\u5b9a\u4e00\u4e2a\u5b57\u6bcd\u4e3a\u4e3b\u5143\uff0c\u7136\u540e\u628a\u5404\u9879\u6309\u8fd9\u4e2a\u5b57\u6bcd\u6b21\u6570\u4ece\u9ad8\u5230\u4f4e\u6392\u5217\uff0c\u518d\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002
\u4f8b10\u3001\u5206\u89e3\u56e0\u5f0fa (b-c)+b (c-a)+c (a-b)
\u5206\u6790\uff1a\u6b64\u9898\u53ef\u9009\u5b9aa\u4e3a\u4e3b\u5143\uff0c\u5c06\u5176\u6309\u6b21\u6570\u4ece\u9ad8\u5230\u4f4e\u6392\u5217
\u89e3\uff1aa (b-c)+b (c-a)+c (a-b)=a (b-c)-a(b -c )+(b c-c b)
=(b-c) [a -a(b+c)+bc]
=(b-c)(a-b)(a-c)
11\u3001 \u5229\u7528\u7279\u6b8a\u503c\u6cd5
\u5c062\u621610\u4ee3\u5165x\uff0c\u6c42\u51fa\u6570P\uff0c\u5c06\u6570P\u5206\u89e3\u8d28\u56e0\u6570\uff0c\u5c06\u8d28\u56e0\u6570\u9002\u5f53\u7684\u7ec4\u5408\uff0c\u5e76\u5c06\u7ec4\u5408\u540e\u7684\u6bcf\u4e00\u4e2a\u56e0\u6570\u5199\u62102\u621610\u7684\u548c\u4e0e\u5dee\u7684\u5f62\u5f0f\uff0c\u5c062\u621610\u8fd8\u539f\u6210x\uff0c\u5373\u5f97\u56e0\u5f0f\u5206\u89e3\u5f0f\u3002
\u4f8b11\u3001\u5206\u89e3\u56e0\u5f0fx^3 +9x^2 +23x+15
\u89e3\uff1a\u4ee4x=2\uff0c\u5219x^3 +9x^2 +23x+15=8+36+46+15=105
\u5c06105\u5206\u89e3\u62103\u4e2a\u8d28\u56e0\u6570\u7684\u79ef\uff0c\u5373105=3\u00d75\u00d77
\u6ce8\u610f\u5230\u591a\u9879\u5f0f\u4e2d\u6700\u9ad8\u9879\u7684\u7cfb\u6570\u4e3a1\uff0c\u800c3\u30015\u30017\u5206\u522b\u4e3ax+1\uff0cx+3\uff0cx+5\uff0c\u5728x=2\u65f6\u7684\u503c
\u5219x^3 +9x^2 +23x+15\u53ef\u80fd=\uff08x+1\uff09\uff08x+3\uff09\uff08x+5\uff09 \uff0c\u9a8c\u8bc1\u540e\u7684\u786e\u5982\u6b64\u3002
12\u3001\u5f85\u5b9a\u7cfb\u6570\u6cd5
\u9996\u5148\u5224\u65ad\u51fa\u5206\u89e3\u56e0\u5f0f\u7684\u5f62\u5f0f\uff0c\u7136\u540e\u8bbe\u51fa\u76f8\u5e94\u6574\u5f0f\u7684\u5b57\u6bcd\u7cfb\u6570\uff0c\u6c42\u51fa\u5b57\u6bcd\u7cfb\u6570\uff0c\u4ece\u800c\u628a\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u3002
\u4f8b12\u3001\u5206\u89e3\u56e0\u5f0fx^4 -x^3 -5x^2 -6x-4
\u5206\u6790\uff1a\u6613\u77e5\u8fd9\u4e2a\u591a\u9879\u5f0f\u6ca1\u6709\u4e00\u6b21\u56e0\u5f0f\uff0c\u56e0\u800c\u53ea\u80fd\u5206\u89e3\u4e3a\u4e24\u4e2a\u4e8c\u6b21\u56e0\u5f0f\u3002
\u89e3\uff1a\u8bbex^4 -x^3 -5x^2 -6x-4=(x^2 +ax+b)(x^2 +cx+d)
= x^4 +(a+c)x^3 +(ac+b+d)x^2 +(ad+bc)x+bd
\u6240\u4ee5 \u89e3\u5f97
\u5219x^4 -x^3 -5x^2 -6x-4 =(x +x+1)(x -2x-4)
\u521d\u5b66\u56e0\u5f0f\u5206\u89e3\u7684\u201c\u56db\u4e2a\u6ce8\u610f\u201d
\u56e0\u5f0f\u5206\u89e3\u521d\u89c1\u4e8e\u4e5d\u5e74\u4e49\u52a1\u6559\u80b2\u4e09\u5e74\u5236\u521d\u4e2d\u6559\u6750\u300a\u4ee3\u6570\u300b\u7b2c\u4e8c\u518c\uff0c\u5728\u521d\u4e8c\u4e0a\u5b66\u671f\u8bb2\u6388\uff0c\u4f46\u5b83\u7684\u5185\u5bb9\u5374\u6e17\u900f\u4e8e\u6574\u4e2a\u4e2d\u5b66\u6570\u5b66\u6559\u6750\u4e4b\u4e2d\u3002\u5b66\u4e60\u5b83\uff0c\u65e2\u53ef\u4ee5\u590d\u4e60\u521d\u4e00\u7684\u6574\u5f0f\u56db\u5219\u8fd0\u7b97\uff0c\u53c8\u4e3a\u672c\u518c\u4e0b\u4e00\u7ae0\u5206\u5f0f\u6253\u597d\u57fa\u7840\uff1b\u5b66\u597d\u5b83\uff0c\u65e2\u53ef\u4ee5\u57f9\u517b\u5b66\u751f\u7684\u89c2\u5bdf\u3001\u6ce8\u610f\u3001\u8fd0\u7b97\u80fd\u529b\uff0c\u53c8\u53ef\u4ee5\u63d0\u9ad8\u5b66\u751f\u7efc\u5408\u5206\u6790\u548c\u89e3\u51b3\u95ee\u9898\u7684\u80fd\u529b\u3002\u5176\u4e2d\u56db\u4e2a\u6ce8\u610f\uff0c\u5219\u5fc5\u987b\u5f15\u8d77\u5e08\u751f\u7684\u9ad8\u5ea6\u91cd\u89c6\u3002
\u56e0\u5f0f\u5206\u89e3\u4e2d\u7684\u56db\u4e2a\u6ce8\u610f\u6563\u89c1\u4e8e\u6559\u6750\u7b2c5\u9875\u548c\u7b2c15\u9875\uff0c\u53ef\u7528\u56db\u53e5\u8bdd\u6982\u62ec\u5982\u4e0b\uff1a\u9996\u9879\u6709\u8d1f\u5e38\u63d0\u8d1f\uff0c\u5404\u9879\u6709\u201c\u516c\u201d\u5148\u63d0\u201c\u516c\u201d\uff0c\u67d0\u9879\u63d0\u51fa\u83ab\u6f0f1\uff0c\u62ec\u53f7\u91cc\u9762\u5206\u5230\u201c\u5e95\u201d\u3002\u73b0\u4e3e\u6570\u4f8b\uff0c\u8bf4\u660e\u5982\u4e0b\uff0c\u4f9b\u53c2\u8003\u3002
\u4f8b1 \u628a\uff0da2\uff0db2\uff0b2ab\uff0b4\u5206\u89e3\u56e0\u5f0f\u3002
\u89e3\uff1a\uff0da2\uff0db2\uff0b2ab\uff0b4\uff1d\uff0d\uff08a2\uff0d2ab\uff0bb2\uff0d4\uff09\uff1d\uff0d\uff08a\uff0db\uff0b2\uff09\uff08a\uff0db\uff0d2\uff09
\u8fd9\u91cc\u7684\u201c\u8d1f\u201d\uff0c\u6307\u201c\u8d1f\u53f7\u201d\u3002\u5982\u679c\u591a\u9879\u5f0f\u7684\u7b2c\u4e00\u9879\u662f\u8d1f\u7684\uff0c\u4e00\u822c\u8981\u63d0\u51fa\u8d1f\u53f7\uff0c\u4f7f\u62ec\u53f7\u5185\u7b2c\u4e00\u9879\u7cfb\u6570\u662f\u6b63\u7684\u3002\u9632\u6b62\u5b66\u751f\u51fa\u73b0\u8bf8\u5982\uff0d9x2\uff0b4y2\uff1d\uff08\uff0d3x\uff092\uff0d\uff082y\uff092\uff1d\uff08\uff0d3x\uff0b2y\uff09\uff08\uff0d3x\uff0d2y\uff09\uff1d\uff083x\uff0d2y\uff09\uff083x\uff0b2y\uff09\u7684\u9519\u8bef?
\u5982\u4f8b2 \u25b3abc\u7684\u4e09\u8fb9a\u3001b\u3001c\u6709\u5982\u4e0b\u5173\u7cfb\u5f0f\uff1a\uff0dc2\uff0ba2\uff0b2ab\uff0d2bc\uff1d0\uff0c\u6c42\u8bc1\u8fd9\u4e2a\u4e09\u89d2\u5f62\u662f\u7b49\u8170\u4e09\u89d2\u5f62\u3002
\u5206\u6790\uff1a\u6b64\u9898\u5b9e\u8d28\u4e0a\u662f\u5bf9\u5173\u7cfb\u5f0f\u7684\u7b49\u53f7\u5de6\u8fb9\u7684\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002
\u8bc1\u660e\uff1a\u2235\uff0dc2\uff0ba2\uff0b2ab\uff0d2bc\uff1d0\uff0c\u2234\uff08a\uff0bc\uff09\uff08a\uff0dc\uff09\uff0b2b\uff08a\uff0dc\uff09\uff1d0\uff0c\u2234\uff08a\uff0dc\uff09\uff08a\uff0b2b\uff0bc\uff09\uff1d0\uff0e
\u53c8\u2235a\u3001b\u3001c\u662f\u25b3abc\u7684\u4e09\u6761\u8fb9\uff0c\u2234a\uff0b2b\uff0bc\uff1e0\uff0c\u2234a\uff0dc\uff1d0\uff0c
\u5373a\uff1dc\uff0c\u25b3abc\u4e3a\u7b49\u8170\u4e09\u89d2\u5f62\u3002
\u4f8b3\u628a\uff0d12x2nyn\uff0b18xn\uff0b2yn\uff0b1\uff0d6xnyn\uff0d1\u5206\u89e3\u56e0\u5f0f\u3002\u89e3\uff1a\uff0d12x2nyn\uff0b18xn\uff0b2yn\uff0b1\uff0d6xnyn\uff0d1\uff1d\uff0d6xnyn\uff0d1\uff082xny\uff0d3x2y2\uff0b1\uff09
\u8fd9\u91cc\u7684\u201c\u516c\u201d\u6307\u201c\u516c\u56e0\u5f0f\u201d\u3002\u5982\u679c\u591a\u9879\u5f0f\u7684\u5404\u9879\u542b\u6709\u516c\u56e0\u5f0f\uff0c\u90a3\u4e48\u5148\u63d0\u53d6\u8fd9\u4e2a\u516c\u56e0\u5f0f\uff0c\u518d\u8fdb\u4e00\u6b65\u5206\u89e3\u56e0\u5f0f\uff1b\u8fd9\u91cc\u7684\u201c1\u201d\uff0c\u662f\u6307\u591a\u9879\u5f0f\u7684\u67d0\u4e2a\u6574\u9879\u662f\u516c\u56e0\u5f0f\u65f6\uff0c\u5148\u63d0\u51fa\u8fd9\u4e2a\u516c\u56e0\u5f0f\u540e\uff0c\u62ec\u53f7\u5185\u5207\u52ff\u6f0f\u63891\u3002\u9632\u6b62\u5b66\u751f\u51fa\u73b0\u8bf8\u59826p\uff08x\uff0d1\uff093\uff0d8p2\uff08x\uff0d1\uff092\uff0b2p\uff081\uff0dx\uff092\uff1d2p\uff08x\uff0d1\uff092\u30143\uff08x\uff0d1\uff09\uff0d4p\u3015\uff1d2p\uff08x\uff0d1\uff092\uff083x\uff0d4p\uff0d3\uff09\u7684\u9519\u8bef\u3002
\u4f8b4 \u5728\u5b9e\u6570\u8303\u56f4\u5185\u628ax4\uff0d5x2\uff0d6\u5206\u89e3\u56e0\u5f0f\u3002
\u89e3\uff1ax4\uff0d5x2\uff0d6\uff1d\uff08x2\uff0b1\uff09\uff08x2\uff0d6\uff09\uff1d\uff08x2\uff0b1\uff09\uff08x\uff0b6\uff09\uff08x\uff0d6\uff09
\u8fd9\u91cc\u7684\u201c\u5e95\u201d\uff0c\u6307\u5206\u89e3\u56e0\u5f0f\uff0c\u5fc5\u987b\u8fdb\u884c\u5230\u6bcf\u4e00\u4e2a\u591a\u9879\u5f0f\u56e0\u5f0f\u90fd\u4e0d\u80fd\u518d\u5206\u89e3\u4e3a\u6b62\u3002\u5373\u5206\u89e3\u5230\u5e95\uff0c\u4e0d\u80fd\u534a\u9014\u800c\u5e9f\u7684\u610f\u601d\u3002\u5176\u4e2d\u5305\u542b\u63d0\u516c\u56e0\u5f0f\u8981\u4e00\u6b21\u6027\u63d0\u201c\u5e72\u51c0\u201d\uff0c\u4e0d\u7559\u201c\u5c3e\u5df4\u201d\uff0c\u5e76\u4f7f\u6bcf\u4e00\u4e2a\u62ec\u53f7\u5185\u7684\u591a\u9879\u5f0f\u90fd\u4e0d\u80fd\u518d\u5206\u89e3\u3002\u9632\u6b62\u5b66\u751f\u51fa\u73b0\u8bf8\u59824x4y2\uff0d5x2y2\uff0d9y2\uff1dy2\uff084x4\uff0d5x2\uff0d9\uff09\uff1dy2\uff08x2\uff0b1\uff09\uff084x2\uff0d9\uff09\u7684\u9519\u8bef\u3002
\u7531\u6b64\u770b\u6765\uff0c\u56e0\u5f0f\u5206\u89e3\u4e2d\u7684\u56db\u4e2a\u6ce8\u610f\u8d2f\u7a7f\u4e8e\u56e0\u5f0f\u5206\u89e3\u7684\u56db\u79cd\u57fa\u672c\u65b9\u6cd5\u4e4b\u4e2d\uff0c\u4e0e\u56e0\u5f0f\u5206\u89e3\u7684\u56db\u4e2a\u6b65\u9aa4\u6216\u8bf4\u4e00\u822c\u601d\u8003\u987a\u5e8f\u7684\u56db\u53e5\u8bdd\uff1a\u201c\u5148\u770b\u6709\u65e0\u516c\u56e0\u5f0f\uff0c\u518d\u770b\u80fd\u5426\u5957\u516c\u5f0f\uff0c\u5341\u5b57\u76f8\u4e58\u8bd5\u4e00\u8bd5\uff0c\u5206\u7ec4\u5206\u89e3\u8981\u5408\u9002\u201d\u662f\u4e00\u8109\u76f8\u627f\u7684\u3002
原式：可以换成x²+（-3）x+2=0 满足a*b=2 a+b=-3 就可以换成（x+a）（x+b）=0 这是思路，希望可以帮到你
乘积为常数项，和为一次项
希望对你有所帮助，有不会的可以再问，祝学习进步！您的及时采纳是对答题者的尊重！
把2拆成－1和－2
x=1 1的平方减去1乘3等于负2，负2加2等于0
x等于1，2
绛旓細1銆佸崄瀛楃浉涔樻硶鐨勬柟娉曪細鍗佸瓧宸﹁竟鐩镐箻绛変簬浜屾椤圭郴鏁帮紝鍙宠竟鐩镐箻绛変簬甯告暟椤癸紝浜ゅ弶鐩镐箻鍐嶇浉鍔犵瓑浜庝竴娆￠」绯绘暟銆2銆佸崄瀛楃浉涔樻硶鐨勭敤澶勶細锛1锛夌敤鍗佸瓧鐩镐箻娉曟潵鍒嗚В鍥犲紡銆傦紙2锛夌敤鍗佸瓧鐩镐箻娉曟潵瑙ｄ竴鍏冧簩娆℃柟绋嬨3銆佸崄瀛楃浉涔樻硶鐨勪紭鐐癸細鐢ㄥ崄瀛楃浉涔樻硶鏉ヨВ棰樼殑閫熷害姣旇緝蹇紝鑳藉鑺傜害鏃堕棿锛岃屼笖杩愮敤绠楅噺涓嶅ぇ锛屼笉瀹规槗鍑洪敊銆...
绛旓細鍗佸瓧鐩镐箻娉曠殑鍏蜂綋鏂规硶锛氬崄瀛楀乏杈圭浉涔樼瓑浜庝簩娆￠」绯绘暟,鍙宠竟鐩镐箻绛変簬甯告暟椤,浜ゅ弶鐩镐箻鍐嶇浉鍔犵瓑浜庝竴娆￠」绯绘暟.搴旂敤鍗佸瓧鐩镐箻娉曡В棰樼殑瀹炰緥锛氫緥1鎶妋²+4m-12鍒嗚В鍥犲紡 鍒嗘瀽锛氭湰棰樹腑甯告暟椤-12鍙互鍒嗕负-1脳12,-2脳6,-3脳4,-4脳3,-6脳2,-12脳1褰-12鍒嗘垚-2脳6鏃,鎵嶇鍚堟湰棰 鍥犱负 1 -2 1 鈺 ...
绛旓細绛旀瑙佷笅鍥撅細
绛旓細鍗佸瓧鐩镐箻娉曟槸涓绉嶇敤浜庡垎瑙ｅ洜寮忕殑鏁板鏂规硶锛岄傜敤浜庣郴鏁颁笉涓1鐨勪簩娆′笁椤瑰紡銆傞氳繃杩欑鏂规硶锛屽彲浠ュ皢涓涓簩娆′笁椤瑰紡鎷嗗垎鎴愪袱涓竴娆″洜寮忕殑涔樼Н锛屼粠鑰岀畝鍖栬В棰樿繃绋嬨備竴銆佺郴鏁颁笉涓轰竴鐨勫崄瀛楃浉涔樻硶鐨勪箻绉叿浣撴楠 1銆佸皢浜屾椤圭郴鏁板垎瑙ｈ川鍥犳暟銆傚浜庝簩娆￠」2x^2 + 3x + 5锛屽皢2鍒嗚В涓2脳1銆2銆佸皢甯告暟椤瑰垎瑙ｈ川...
绛旓細鍙互鐢ㄥ崄瀛楃浉涔樻硶鍒嗚В鍥犲紡銆傚崄瀛楃浉涔樻硶 瑙: 2x²-5x+3=0 (2x-3)(x-1)=0 2x-3=0锛寈=3/2锛涙垨鑰厁-1=0锛寈=1 鍘熸柟绋嬬殑瑙ｆ槸x=3/2鍜寈=1銆
绛旓細鍗佸瓧鐩镐箻娉鈥斺斿熷姪鐢诲崄瀛椾氦鍙夌嚎鍒嗚В绯绘暟锛屼粠鑰屾妸浜屾涓夐」寮忓垎瑙ｅ洜寮忕殑鏂规硶鍙仛鍗佸瓧鐩镐箻娉曘傚崄瀛楃浉涔樻硶鏄簩娆′笁椤瑰紡鍒嗚В鍥犲紡鐨勪竴绉嶅父鐢ㄦ柟娉曪紝瀹冩槸鍏堝皢浜屾涓夐」寮 鐨勪簩娆￠」绯绘暟a鍙婂父鏁伴」c閮藉垎瑙ｄ负涓や釜鍥犳暟鐨勪箻绉紙涓鑸細鏈夊嚑绉嶄笉鍚岀殑鍒嗘硶锛夌劧鍚庢寜鏂滅嚎浜ゅ弶鐩镐箻銆佸啀鐩稿姞锛岃嫢鏈 锛屽垯鏈 锛屽惁鍒欙紝闇...
绛旓細浜屾椤瑰拰甯告暟椤瑰垎鍒媶鍒嗭紝鐒跺悗瑕佹弧瓒充氦鍙鐩镐箻鍐嶇浉鍔犵瓑浜庝竴娆￠」
绛旓細1銆佸崄瀛楃浉涔樻硶鐨勬柟娉曟槸鍗佸瓧宸﹁竟鐩镐箻绛変簬浜屾椤圭郴鏁锛屽彸杈圭浉涔樼瓑浜庡父鏁伴」锛屼氦鍙夌浉涔樺啀鐩稿姞绛変簬涓娆￠」绯绘暟銆2銆佸崄瀛楃浉涔樻硶鐨勭敤澶勬槸鐢ㄥ崄瀛楃浉涔樻硶鏉ュ垎瑙ｅ洜寮鎴栫敤鍗佸瓧鐩镐箻娉曟潵瑙ｄ竴鍏冧簩娆℃柟绋嬨3銆佸崄瀛楃浉涔樻硶鐨勪紭鐐规槸鐢ㄥ崄瀛楃浉涔樻硶鏉ヨВ棰樼殑閫熷害姣旇緝蹇紝鑳藉鑺傜害鏃堕棿锛岃屼笖杩愮敤绠楅噺涓嶅ぇ锛屼笉瀹规槗鍑洪敊銆4銆佸崄瀛楃浉涔...
绛旓細鈥滃崄瀛楃浉涔樻硶鈥濈敤浜庝竴鍏冧簩娆℃柟绋嬬殑姹傝В锛屾槸鍥犲紡鍒嗚В鐨勬柟娉曚箣涓锛岀啛缁冩帉鎻¤兘鎴愬嶆彁鍗囪绠楅熷害锛佷竴銆佸熀鏈師鐞 浜屻佷娇鐢ㄦ柟娉 杩愮敤涓婅堪绛夊紡鐨勯嗚繍绠楋紝鍦ㄤ粎浠呭凡鐭ョ瓑鍙峰彸杈圭殑鍐呭鎶婂乏杈圭殑寮忓瓙鍑戝嚭鏉ャ傚嵆锛鍗佸瓧宸﹁竟鐩镐箻绛変簬浜屾椤圭郴鏁锛屽彸杈圭浉涔樼瓑浜庡父鏁伴」锛屼氦鍙夌浉涔樺啀鐩稿姞绛変簬涓娆￠」绯绘暟銆傝繖鍙ヨ瘽浠涔堟剰鎬濓紝鐢ㄦ枃瀛...
绛旓細鍒嗗埆鍐欏湪鍗佸瓧浜ゅ弶绾跨殑宸︿笂瑙掑拰宸︿笅瑙掞紝鍐嶅垎瑙ｅ父鏁伴」锛屽垎 鍒啓鍦ㄥ崄瀛椾氦鍙夌嚎鐨勫彸涓婅鍜屽彸涓嬭锛岀劧鍚庝氦鍙鐩镐箻锛屾眰浠ｆ暟鍜岋紝浣垮叾绛変簬涓娆￠」绯绘暟. 鍒嗚В浜屾椤圭郴鏁(鍙彇姝ｅ洜鏁)锛 2锛1脳2锛2脳1锛 鍒嗚В甯告暟椤癸細 3=1脳3=1脳3==(锛3)脳(锛1)=(锛1)脳(锛3). 鐢ㄧ敾鍗佸瓧浜ゅ弶绾鏂规硶...
