数学十字相乘的技巧和方法 数学十字相乘怎么配
\u6570\u5b66\u201c\u5341\u5b57\u76f8\u4e58\u201d\u7684\u65b9\u6cd5\u5341\u5b57\u76f8\u4e58\u6cd5\u867d\u7136\u6bd4\u8f83\u96be\u5b66,\u4f46\u662f\u4e00\u65e6\u5b66\u4f1a\u4e86\u5b83,\u7528\u5b83\u6765\u89e3\u9898,\u4f1a\u7ed9\u6211\u4eec\u5e26\u6765\u5f88\u591a\u65b9\u4fbf,\u4ee5\u4e0b\u662f\u6211\u5bf9\u5341\u5b57\u76f8\u4e58\u6cd5\u63d0\u51fa\u7684\u4e00\u4e9b\u4e2a\u4eba\u89c1\u89e3\u3002
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
\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-2y)(7x-9y)
\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
\u6ce8\u610f
1.\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u628a\u67d0\u4e9b\u5f62\u5982ax2+bx+c\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u5e94\u6ce8\u610f\u4ee5\u4e0b\u95ee\u9898\uff1a
(1)\u6b63\u786e\u7684\u5341\u5b57\u76f8\u4e58\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a
a1 c1
\u5728\u5f0f\u5b50 � \u4e2d\uff0c\u7ad6\u5411\u7684\u4e24\u4e2a\u6570\u5fc5\u987b\u6ee1\u8db3\u5173\u7cfba1a2=a\uff0cc1c2=c\uff1b\u5728\u4e0a\u5f0f\u4e2d\uff0c\u659c\u5411\u7684
a2 c2
\u4e24\u4e2a\u6570\u5fc5\u987b\u6ee1\u8db3\u5173\u7cfba1c2+a2c1=b.
(2)\u7531\u5341\u5b57\u76f8\u4e58\u7684\u56fe\u4e2d\u7684\u56db\u4e2a\u6570\u5199\u51fa\u5206\u89e3\u540e\u7684\u4e24\u4e2a\u4e00\u6b21\u56e0\u5f0f\u65f6\uff0c\u56fe\u7684\u4e0a\u4e00\u884c\u4e24\u4e2a\u6570\u4e2d\uff0ca1\u662f\u7b2c\u4e00\u4e2a\u56e0\u5f0f\u4e2d\u7684\u4e00\u6b21\u9879\u7cfb\u6570\uff0cc1\u662f\u5e38\u6570\u9879\uff1b\u5728\u4e0b\u4e00\u884c\u7684\u4e24\u4e2a\u6570\u4e2d\uff0ca2\u662f\u7b2c\u4e8c\u4e2a\u56e0\u5f0f\u4e2d\u7684\u4e00\u6b21\u9879\u7684\u7cfb\u6570\uff0cc2\u662f\u5e38\u6570\u9879.
(3)\u4e8c\u6b21\u9879\u7cfb\u6570a\u4e00\u822c\u90fd\u628a\u5b83\u770b\u4f5c\u662f\u6b63\u6570(\u5982\u679c\u662f\u8d1f\u6570\uff0c\u5219\u5e94\u63d0\u51fa\u8d1f\u53f7\uff0c\u5229\u7528\u6052\u7b49\u53d8\u5f62\u628a\u5b83\u8f6c\u5316\u4e3a\u6b63\u6570\uff0c)\u53ea\u9700\u628a\u5b83\u5206\u89e3\u6210\u4e24\u4e2a\u6b63\u7684\u56e0\u6570.
2.\u5f62\u5982x+px+q\u7684\u67d0\u4e9b\u4e8c\u6b21\u4e09\u9879\u5f0f\u4e5f\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f.
3.\u51e1\u662f\u53ef\u7528\u4ee3\u6362\u7684\u65b9\u6cd5\u8f6c\u5316\u4e3a\u4e8c\u6b21\u4e09\u9879\u5f0fax+bx+c\u7684\u591a\u9879\u5f0f\uff0c\u6709\u4e9b\u4e5f\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\uff0c\u5982\u4f8b4.
\u5341\u5b57\u76f8\u4e58\u6cd5\u867d\u7136\u6bd4\u8f83\u96be\u5b66,\u4f46\u662f\u4e00\u65e6\u5b66\u4f1a\u4e86\u5b83,\u7528\u5b83\u6765\u89e3\u9898,\u4f1a\u7ed9\u6211\u4eec\u5e26\u6765\u5f88\u591a\u65b9\u4fbf,\u4ee5\u4e0b\u662f\u6211\u5bf9\u5341\u5b57\u76f8\u4e58\u6cd5\u63d0\u51fa\u7684\u4e00\u4e9b\u4e2a\u4eba\u89c1\u89e3\u3002
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
\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
多做就会了要的是熟练么技巧可言
绛旓細鈶犵涓姝ユ壘鍏洜寮忓彲鎸夌収纭畾鍏洜寮忕殑鏂规硶鍏堢‘瀹氱郴鏁板湪纭畾瀛楁瘝锛涒憽绗簩姝ユ彁鍏洜寮忓苟纭畾鍙︿竴涓洜寮忥紝娉ㄦ剰瑕佺‘瀹氬彟涓涓洜寮忥紝鍙敤鍘熷椤瑰紡闄や互鍏洜寮忥紝鎵寰楃殑鍟嗗嵆鏄彁鍏洜寮忓悗鍓╀笅鐨勪竴涓洜寮忥紝涔熷彲鐢ㄥ叕鍥犲紡鍒嗗埆闄ゅ幓鍘熷椤瑰紡鐨勬瘡涓椤癸紝姹傜殑鍓╀笅鐨勫彟涓涓洜寮忥紱鈶㈡彁瀹屽叕鍥犲紡鍚庯紝鍙︿竴鍥犲紡鐨勯」鏁颁笌鍘熷椤...
绛旓細1銆佸揩閫熻绠椾箻娉曪細褰撻渶瑕佽绠椾袱涓緝澶х殑澶氫綅鏁扮浉涔樻椂锛屼娇鐢ㄥ崄瀛楃浉涔樻硶鍙互绠鍖栬绠楄繃绋嬶紝鍑忓皯鍑洪敊鐨勫彲鑳芥с2銆佺被浼煎崟椤瑰紡鐨勪箻娉曪細鍦ㄤ唬鏁板涓紝鍗佸瓧鐩镐箻娉曚篃鍙互甯姪璁$畻绫讳技鍗曢」寮忕殑涔樻硶锛岀壒鍒槸瀵逛簬鍚湁鍙橀噺鐨勮〃杈惧紡锛屽澶氶」寮忕殑涔樻硶銆3銆佹暀瀛﹁緟鍔╁伐鍏凤細鍗佸瓧鐩镐箻娉曞彲浠ヤ綔涓轰竴绉嶆暀瀛﹁緟鍔╁伐鍏凤紝鐢ㄤ簬鍚戝鐢熶滑浠...
绛旓細鍗佸瓧宸﹁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
绛旓細鍗佸瓧鐩镐箻娉曟槸鍥犲紡鍒嗚В涓崄鍥涚鏂规硶涔嬩竴,鍙﹀鍗佷笁绉嶅垎鍒兘鏄:1.鎻愬叕鍥犲紡娉 2.鍏紡娉 3.鍙屽崄瀛楃浉涔樻硶 4.杞崲瀵圭О娉 5.鎷嗘坊椤规硶 6.閰嶆柟娉7.鍥犲紡瀹氱悊娉 8.鎹㈠厓娉 9.缁煎悎闄ゆ硶 10.涓诲厓娉 11.鐗规畩鍊兼硶 12.寰呭畾绯绘暟娉 13.浜屾澶氶」寮忋傚崄瀛楀垎瑙f硶鐨勬柟娉曠畝鍗曟潵璁插氨鏄:鍗佸瓧宸﹁竟鐩镐箻绛変簬浜屾椤圭郴鏁,鍙宠竟鐩镐箻绛変簬...
绛旓細鍗佸瓧鐩镐箻娉曠殑鏂规硶绠鍗曠偣鏉ヨ灏辨槸:鍗佸瓧宸﹁竟鐩镐箻绛変簬浜屾椤圭郴鏁,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¢」绯绘暟銆 鍗佸瓧鐩镐箻娉曡兘鎶婃煇浜涗簩娆′笁椤瑰紡鍒嗚В鍥犲紡銆傝繖绉嶆柟娉曠殑鍏抽敭鏄妸浜屾椤圭郴鏁癮鍒嗚В鎴愪袱 鍗佸瓧鐩镐箻娉曚釜鍥犳暟a1,a2鐨勭Нa1.a2,鎶婂父鏁伴」c鍒嗚В鎴愪袱涓洜鏁癱1,c2鐨勭Нc1涔榗2,骞朵娇a1c2+a2c1姝eソ鏄竴娆¢」b,閭...
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鍗佸瓧鐩镐箻娉曠殑涔樼Н鍏蜂綋姝ラ 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...
绛旓細鍗佸瓧鐩镐箻娉曠殑鍏蜂綋鏂规硶锛鍗佸瓧宸﹁竟鐩镐箻绛変簬浜屾椤圭郴鏁,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 ...
绛旓細鎴戜滑鍗佸瓧鐩镐箻鏁欎簡涓ゆ锛屾柟娉曚笉鍚岋紝鎴戝氨鎷胯緝绠鍗曢偅绉嶅惂 鍗佸瓧鐩镐箻娉曞彛浠わ細澶疵楀ご浣滃ご锛屽熬脳灏句綔灏撅紝浜ゅ弶鐩镐箻鐩稿姞浣滀竴娆¢」 渚嬶細x²-4x+3=0 瑙o細锛 锛夛紙 锛=0 x 鈺测暠 锛焫 鈺扁暡 锛燂紵x+锛焫=-4x 棣栧厛鎶婅繖涓垪鍑烘潵锛岀劧鍚庢牴鎹彛浠わ紝灏久楀熬浣滃熬锛屽緱鍑1脳3绛変簬3 鎵浠 x 鈺测暠 1...
绛旓細鍗佸瓧鐩镐箻娉 杩欑鏂规硶鏈変袱绉嶆儏鍐点傗憼x^2+(p+q)x+pq鍨嬬殑寮忓瓙鐨勫洜寮忓垎瑙 杩欑被浜屾涓夐」寮忕殑鐗圭偣鏄細浜屾椤圭殑绯绘暟鏄1锛涘父鏁伴」鏄袱涓暟鐨勭Н锛涗竴娆¢」绯绘暟鏄父鏁伴」鐨勪袱涓洜鏁扮殑鍜屻傚洜姝わ紝鍙互鐩存帴灏嗘煇浜涗簩娆¢」鐨勭郴鏁版槸1鐨勪簩娆′笁椤瑰紡鍥犲紡鍒嗚В锛歺^2+(p+q)x+pq=(x+p)(x+q) 锛庘憽kx^2+mx+n...
绛旓細鍗佸瓧鐩镐箻娉曠殑鏂规硶绠鍗曟潵璁插氨鏄細鍗佸瓧宸﹁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」锛浜ゅ弶鐩镐箻鍐嶇浉鍔犵瓑浜庝竴娆¢」銆傚叾瀹炲氨鏄繍鐢ㄤ箻娉曞叕寮忚繍绠楁潵杩涜鍥犲紡鍒嗚В銆傚彲鏄棶棰樺湪浜 杩欎釜棰樹笉閫傚悎鍥犲紡鍒嗚В 锛屽亣濡傛槸 2x^2+7x+3=0 鏄彲浠ョ殑 2x 1 x 3 浜ゅ弶鐩镐箻鍐嶇浉鍔 2x*3+x*1=7x锛堟濂斤級锛2x+1锛夛紙x+3...