数学十字交叉法怎么算,能给我举几个例子吗?最好还有解析。 十字交叉法的数学应用

\u5341\u5b57\u4ea4\u53c9\u6cd5\u7684\u6570\u5b66\u539f\u7406\u53ca\u5b9e\u9645\u5e94\u7528

\u5341\u5b57\u4ea4\u53c9\u6cd5\u4e13\u9898\u5341\u5b57\u4ea4\u53c9\u6cd5\u53ef\u9002\u7528\u4e8e\u89e3\u4e24\u79cd\u6574\u4f53\u7684\u6df7\u5408\u7684\u76f8\u5173\u8bd5\u9898\uff0c\u57fa\u672c\u539f\u7406\u5982\u4e0b\uff1a

\u6df7\u5408\u524d
\u6574\u4f53\u4e00\uff0c\u6570\u91cfx\uff0c\u6307\u6807\u91cfa

\u6574\u4f53\u4e8c\uff0c\u6570\u91cfy\uff0c\u6307\u6807\u91cfb\uff08a>b\uff09

\u6df7\u5408\u540e

\u6574\u4f53\uff0c\u6570\u91cf\uff08x+y\uff09\uff0c\u6307\u6807\u91cfc

\u53ef\u5f97\u5230\u5982\u4e0b\u5173\u7cfb\u5f0f\uff1a

x\u00d7a+y\u00d7b=\uff08x+y\uff09c

\u63a8\u51fa\uff1a

x\u00d7\uff08a-c\uff09=y\u00d7\uff08c-b\uff09

\u5f97\u5230\u516c\u5f0f\uff1a

\uff08a-c\uff09\uff1a\uff08c-b\uff09=y\uff1ax

\u5219\u4efb\u610f\u77e5\u9053x\u3001y\u3001a\u3001b\u3001c\u4e2d\u7684\u56db\u4e2a\uff0c\u53ef\u4ee5\u6c42\u51fa\u672a\u77e5\u91cf\u3002\u4e0d\u8fc7\uff0c\u6c42\uff43\u7684\u8bdd\uff0c\u76f4\u63a5\u8ba1\u7b97\u66f4\u4e3a\u7b80\u5355\u3002\u5f53\u77e5\u9053x+y\u65f6\uff0cx\u6216y\u4efb\u610f\u77e5\u9053\u4e00\u4e2a\u4e5f\u53ef\u91c7\u7528\u6b64\u6cd5\uff1b\u77e5\u9053\uff58\uff1a\uff59\u4e5f\u53ef\u4ee5\u3002

\u76f8\u5173\u7684\u6307\u6807\u91cf\u53ef\u4ee5\u662f\u5e73\u5747\u503c\u3001\u6d53\u5ea6\u7b49\u7b49\u3002\u4e3e\u4f8b\u5982\u4e0b\uff1a
1\uff0e\u6c42\u6307\u6807\u91cfa\u3001b\u4e4b\u4e00

\u4f8b1\uff0e\u7532\u5bb9\u5668\u4e2d\u6709\u6d53\u5ea6\u4e3a4%\u7684\u76d0\u6c34150\u514b\uff0c\u4e59\u5bb9\u5668\u4e2d\u6709\u67d0\u79cd\u6d53\u5ea6\u7684\u76d0\u6c34\u82e5\u5e72\uff0c\u4ece\u4e59\u4e2d\u53d6\u51fa450\u514b\u76d0\u6c34\u653e\u5165\u7532\u4e2d\u6df7\u6210\u6d53\u5ea6\u4e3a8.2%\u7684\u76d0\u6c34\uff0c\u95ee\u4e59\u5bb9\u5668\u4e2d\u76d0\u6c34\u7684\u6d53\u5ea6\u662f\u591a\u5c11\uff1f

A.9.6% B.9.8% C.9.9% D.10%

\u89e3\u6790\uff1a\u5df2\u77e5\u4ece\u4e59\u5bb9\u5668\u4e2d\u53d6\u51fa\u7684\u76d0\u6c34\u91cfx=450\uff0c\u7532\u5bb9\u5668\u4e2d\u539f\u6709\u76d0\u6c34\u91cfy=150\uff0c\u7532\u5bb9\u5668\u4e2d\u539f\u6709\u76d0\u6c34\u6d53\u5ea6b=4%\uff0c\u6df7\u5408\u540e\u76d0\u6c34\u6d53\u5ea6c=8.2%\uff0c\u53ef\u5f97\u5230\uff08a-8.2%\uff09\uff1a\uff088.2%-4%\uff09=150\uff1a450\uff0c\u5219b-8.2%=4.2%\u00f73=1.4%\uff0c\u5373\u4e59\u5bb9\u5668\u4e2d\u76d0\u6c34\u6d53\u5ea6b=9.6%

\u6b63\u786e\u7b54\u6848\uff1aA

\u4f8b2\uff0e\u67d0\u8f66\u95f4\u8fdb\u884c\u5b63\u5ea6\u8003\u6838\uff0c\u6574\u4e2a\u8f66\u95f4\u5e73\u5747\u5206\u662f85\u5206\uff0c\u5176\u4e2d2\uff0f3\u7684\u4eba\u5f9780\u5206\u4ee5\u4e0a(\u542b80\u5206)\uff0c\u4ed6\u4eec\u7684\u5e73\u5747\u5206\u662f90\u5206\uff0c\u5219\u4f4e\u4e8e80\u5206\u7684\u4eba\u7684\u5e73\u5747\u5206\u662f\u591a\u5c11?

A\uff0e68 B\uff0e70 C.75 D\uff0e78

\u89e3\u6790\uff1a 90 10 2
85
x 5 1
x=75


\u6b63\u786e\u7b54\u6848\uff1aC

2\uff0e\u6c42\u6570\u91cfx\u3001y\u4e4b\u4e00

\u4f8b1\uff0e\u8f66\u95f4\u517140\u4eba\uff0c\u67d0\u6b21\u6280\u672f\u64cd\u4f5c\u8003\u6838\u7684\u5e73\u5747\u6210\u7ee9\u4e3a80\u5206\uff0c\u5176\u4e2d\u7537\u5de5\u5e73\u5747\u6210\u7ee9\u662f83\u5206\uff0c\u5973\u5de5\u5e73\u5747\u6210\u7ee9\u4e3a78\u5206\uff0c\u8be5\u8f66\u95f4\u6709\u5973\u5de5\u591a\u5c11\u4eba\uff1f

A.16\u4eba B.18\u4eba C.20\u4eba D.24\u4eba

\u89e3\u6790\uff1a\u5df2\u77e5\u7537\u5de5\u5e73\u5747\u6210\u7ee9a=83\uff0c\u5973\u5de5\u5e73\u5747\u6210\u7ee9b=78\uff0c\u603b\u5e73\u5747\u6210\u7ee9c=80\uff0c\u8f66\u95f4\u603b\u4eba\u6570x+y=40\uff0c\u5219y\uff1ax=\uff0883-80\uff09\uff1a\uff0880-78\uff09=3\uff1a2\uff0c\u5219\u5973\u5de5\u4eba\u6570y=40\u00d73\u00f7\uff083+2\uff09=24\u4eba\u3002

\u6b63\u786e\u7b54\u6848\uff1aD

\u4f8b2\uff0e\u6709\u6d53\u5ea6\u4e3a4%\u7684\u76d0\u6c34\u82e5\u5e72\u514b\uff0c\u84b8\u53d1\u4e86\u4e00\u4e9b\u6c34\u5206\u540e\u6d53\u5ea6\u53d8\u621010%\uff0c\u518d\u52a0\u5165300\u514b4%\u7684\u76d0\u6c34\u540e\uff0c\u6d53\u5ea6\u53d8\u4e3a6.4%\u7684\u76d0\u6c34\uff0c\u95ee\u6700\u521d\u7684\u76d0\u6c34\u591a\u5c11\u514b?

A.200\u514b B.300\u514b C.400\u514b D.500\u514b

\u89e3\u6790\uff1a\u5df2\u77e5\u539f\u6709\u76d0\u6c34\u84b8\u53d1\u540e\u6d53\u5ea6a=10%\uff0c\u52a0\u5165\u7684\u76d0\u6c34\u6d53\u5ea6\u4e3ab=4%\uff0c\u91cd\u91cf\u4e3ay=300\u514b\uff0c\u6df7\u5408\u540e\u76d0\u6c34\u6d53\u5ea6c=6.4%\uff0c\u5219y\uff1ax=\uff0810%-6.4%\uff09\uff1a\uff086.4%-4%\uff09=3\uff1a2\uff0c\u5219\u539f\u6709\u76d0\u6c34\u84b8\u53d1\u540e\u4e3a300\u00f73\u00d72=200\u514b\uff0c\u6700\u521d\u76d0\u6c34\u4e3a200\u00d710%\u00f74%=500\u514b\u3002

\u6b63\u786e\u7b54\u6848\uff1aD









1 \u67d0\u5e02\u73b0\u670970\u4e07\u4eba\u53e3\uff0c\u5982\u679c5\u5e74\u540e\u57ce\u9547\u4eba\u53e3\u589e\u52a04%\uff0c\u519c\u6751\u4eba\u53e3\u589e\u52a05.4%\uff0c\u5219\u5168\u5e02\u4eba\u53e3\u5c06\u589e\u52a04.8%\uff0c\u90a3
\u8fd9\u4e2a\u57ce\u5e02\u73b0\u6709\u57ce\u9547\u4eba\u53e3\u591a\u5c11\uff1f
A30B31.2C40D41.6
\u8bbe\u73b0\u6709\u57ce\u9547\u4eba\u53e3X\u4e07
\u57ce\u5e02X 4% 0.6%
4.8% 0.6%/0.8%=3/4 \u5373X\u4e3a30\u4e07\u4eba
\u5bb6\u675170-X 5.4% 0.8%

2 \u4e00\u5757\u8bd5\u9a8c\u7530\uff0c\u4ee5\u524d\u8fd9\u5757\u5730\u6240\u79cd\u690d\u7684\u662f\u666e\u901a\u6c34\u7a3b\u3002\u73b0\u5728\u5c06\u8be5\u8bd5\u9a8c\u7530\u76841/3\u79cd\u4e0a\u8d85\u7ea7\u6c34\u7a3b\uff0c\u6536\u5272\u65f6\u53d1\u73b0\u8bd5\u9a8c\u7530\u6c34\u7a3b\u603b\u4ea7\u91cf\u662f\u4ee5\u524d\u603b\u4ea7\u91cf\u76841.5\u500d\u3002\u5982\u679c\u666e\u901a\u6c34\u7a3b\u7684\u4ea7\u91cf\u4e0d\u53d8\uff0c\u90a3\u4e48\u8d85\u7ea7\u6c34\u7a3b\u7684\u5e73\u5747\u4ea7\u91cf\u4e0e\u666e\u901a\u6c34\u7a3b\u7684\u5e73\u5747\u4ea7\u91cf\u4e4b\u6bd4\u662f\uff08 \uff09\u3002
A\uff0e5\uff1a2 B\u30014\uff1a3 C\u30013\uff1a1 D\u30012\uff1a1
\u8bbe\u8d85\u7ea7\u6c34\u7a3b\u7684\u5e73\u5747\u4ea7\u91cf\u662f\u666e\u901a\u6c34\u7a3b\u7684X\u500d
\u8d85\u7ea7\u6c34\u7a3b X 0.5 1/3
1.5 0.5/X-1.5=1/3/2/3 X=2.5
1 X-1.5 2/3
3 \u67d0\u73ed\u7537\u751f\u6bd4\u5973\u751f\u4eba\u6570\u591a80%\uff0c\u4e00\u6b21\u8003\u8bd5\u540e\uff0c\u5168\u73ed\u5e73\u5747\u6210\u7ea7\u4e3a75 \u5206\uff0c\u800c\u5973\u751f\u7684\u5e73\u5747\u5206\u6bd4\u7537\u751f\u7684\u5e73\u5747\u5206\u9ad820% \uff0c\u5219\u6b64\u73ed\u5973\u751f\u7684\u5e73\u5747\u5206\u662f\uff1a

\u3000\u3000A \uff0e84 \u5206\u3000\u3000B . 85 \u5206 \u3000\u3000C . 86 \u5206 \u3000\u3000D . 87 \u5206
\u6839\u636e\u7537\u751f\u6bd4\u5973\u751f\u4eba\u6570\u591a80%.\u56e0\u6b64\u7537\u5973\u751f\u4eba\u6570\u6bd4\u4e3a180:100=9:5
\u8bbe\u7537\u751f\u5e73\u5747\u5206\u662fX,\u5219\u7531\u5973\u751f\u7684\u5e73\u5747\u5206\u6bd4\u7537\u751f\u7684\u5e73\u5747\u5206\u9ad820%,\u5973\u751f\u5e73\u5747\u5206\u65701.2X
\u7537\u751f X 1.2X-75 9
75 1.2X-75/75-X=9/5 X=70
\u5973\u751f 1.2X 75-X
1.2X=1.2*70=84 ,\u56e0\u6b64\u5973\u751f\u7684\u5e73\u5747\u5206\u4e3a84\u5206
4 \u67d0\u673a\u5173\u5171\u6709\u5e72\u90e8\u804c\u5de5350\u4eba\uff0c\u5176\u4e2d55\u5c81\u4ee5\u4e0a\u5171\u670970\u4eba\u3002\u73b0\u62df\u8fdb\u884c\u673a\u6784\u6539\u9769\uff0c\u603b\u4f53\u89c4\u6a21\u538b\u7f29\u4e3a180\u4eba\uff0c\u5e76\u89c4\u5b9a55\u5c81\u4ee5\u4e0a\u7684\u4eba\u88c1\u51cf\u6bd4\u4f8b\u4e3a70%\u3002\u8bf7\u95ee55\u5c81\u4ee5\u4e0b\u7684\u4eba\u88c1\u51cf\u6bd4\u4f8b\u7ea6\u662f\u591a\u5c11\uff1f\uff08 \uff09
A.51% B.43% C.40% D.34%
\u8bbe55\u5c81\u4ee5\u4e0b\u7684\u4eba\u88c1\u51cf\u6bd4\u4f8b\u4e3aX,
>55\u5c81 70% 17/35-X 70
170/350 17/35-X/3/14=70/280 X=121/280
<55\u5c81 X 3/14 280
121/280~43%
5 \u67d0\u5e02\u5c45\u6c11\u751f\u6d3b\u7528\u7535\u6bcf\u6708\u6807\u51c6\u7528\u7535\u91cf\u7684\u57fa\u672c\u4ef7\u683c\u4e3a\u6bcf\u5ea60.50\u5143\uff0c\u82e5\u6bcf\u6708\u7528\u7535\u91cf\u8d85\u8fc7\u6807\u51c6\u7528\u7535\u91cf\uff0c\u8d85\u51fa\u90e8\u5206\u6309\u57fa\u672c\u4ef7\u683c\u768480\uff05\u6536\u8d39\uff0c\u67d0\u6237\u4e5d\u6708\u4efd\u7528\u753584\u5ea6\uff0c\u5171\u4ea4\u7535\u8d3939.6\u5143\uff0c\u5219\u8be5\u5e02\u6bcf\u6708\u6807\u51c6\u7528\u7535\u91cf\u4e3a\uff08 \uff09\u3002
A\uff0e60\u5ea6 B\uff0e65\u5ea6 C\uff0e70\u5ea6 D\uff0e75\u5ea6
\u8bbe\u6bcf\u6708\u6807\u51c6\u7528\u7535X\u5ea6
\u57fa\u7840 0.5 5/70 X
39.6/84 5/70/2/70=X/84-X X=60
\u6298\u6263 0.5*80% 2/70 84-X
6 \u67d0\u4f53\u80b2\u8bad\u7ec3\u4e2d\u5fc3\uff0c\u6559\u7ec3\u5458\u4e2d\u7537\u536090\uff05\uff0c\u8fd0\u52a8\u5458\u4e2d\u7537\u536080\uff05\uff0c\u5728\u6559\u7ec3\u5458\u548c\u8fd0\u52a8\u5458\u4e2d\u7537\u536082\uff05\uff0c\u6559\u7ec3\u5458\u4e0e\u8fd0\u52a8\u5458\u4eba\u6570\u4e4b\u6bd4\u662f

A\uff0e2\uff1a5 B\uff0e1\uff1a3 C\uff0e1\uff1a4 D\uff0e1\uff1a5
\u6559\u7ec3 90% 2% N\u6559
82% N\u6559/N\u961f=2%/8%=1:4
\u961f\u5458 80% 8% N\u961f
7 \u4e00\u53ea\u732b\u6bcf\u5929\u5403\u7531\u98df\u54c1A\u548c\u98df\u54c1B\u6405\u62cc\u6210\u7684\u98df\u7269300\u514b,\u98df\u54c1A\u7684\u86cb\u767d\u8d28\u542b\u91cf\u4e3a10%,\u98df\u54c1B\u7684\u86cb\u767d\u8d28\u542b\u91cf\u4e3a15%,\u5982\u679c\u8be5\u732b\u6bcf\u5929\u9700\u898138\u514b\u86cb\u767d\u8d28,\u95ee\u98df\u7269\u4e2d\u98df\u54c1A\u7684\u6bd4\u91cd\u662f\u767e\u5206\u4e4b\u51e0?
A47%B40%C1/3D50%
\u98df\u54c1A 10% 7/300 Na
38/300 Na/Nb=7/300/8/300=7/8
\u98df\u54c1B 15% 8/300 Nb
7/7+8 *100~ 47%

十字相乘法能把二次三项式分解因式。要务必注意各项系数的符号,以及写在十字交叉线四个部分的项。
把2x²-7x+3分解因式.
分析:先分解二次项系数,分别写在十字交叉线的左上角和左下角,再分解常数项,分
别写在十字交叉线的右上角和右下角,然后交叉相乘,求代数和,使其等于一次项系数.
分解二次项系数(只取正因数 因为取负因数的结果与正因数结果相同!)。
2=1×2=2×1;
分解常数项:
3=1×3=3×1=(-3)×(-1)=(-1)×(-3).
用画十字交叉线方法表示下列四种情况:
1 1

2 3
1×3+2×1=5 ≠-7
1 3

2 1
1×1+2×3=7 ≠-7
1 -1

2 -3
1×(-3)+2×(-1)=-5 ≠-7
1 -3

2 -1
1×(-1)+2×(-3)=-7
经过观察,第四种情况是正确的,这是因为交叉相乘后,两项代数和恰等于一次项系数-7。
解 2x²-7x+3=(x-3)(2x-1)

http://baike.baidu.com/link?url=15HR4uAaE8ykyZyL961hlhRnJXxKq--QssYVqWdJ4t6CGklJ5MQxs3HjYC4EKAwHKCS1mdpnfhP2A_f2VhHvBa



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