求解关于x的方程
\u89e3\u5173\u4e8ex\u7684\u65b9\u7a0b\uff1am-6/x-2=2
m-6/x=4
6/x=m-4
x=6/(m-4)
\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u57fa\u672c\u601d\u60f3\u65b9\u6cd5\u662f\u901a\u8fc7\u201c\u964d\u6b21\u201d\u5c06\u5b83\u5316\u4e3a\u4e24\u4e2a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u3002\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u6709\u56db\u79cd\u89e3\u6cd5\uff1a \u3000\u30001\u3001\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\uff1b2\u3001\u914d\u65b9\u6cd5\uff1b3\u3001\u516c\u5f0f\u6cd5\uff1b4\u3001\u56e0\u5f0f\u5206\u89e3\u6cd5\u3002 \u3000\u30001\u3001\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\uff1a \u3000\u3000\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\u5c31\u662f\u7528\u76f4\u63a5\u5f00\u5e73\u65b9\u6c42\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u65b9\u6cd5\u3002\u7528\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\u89e3\u5f62\u5982(x-m)^2;=n (n\u22650)\u7684 \u65b9\u7a0b\uff0c\u5176\u89e3\u4e3ax=\u00b1\u221an+m . \u3000\u3000\u4f8b1\uff0e\u89e3\u65b9\u7a0b\uff081\uff09(3x+1)^2;=7 \uff082\uff099x^2;-24x+16=11 \u3000\u3000\u5206\u6790\uff1a\uff081\uff09\u6b64\u65b9\u7a0b\u663e\u7136\u7528\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\u597d\u505a\uff0c\uff082\uff09\u65b9\u7a0b\u5de6\u8fb9\u662f\u5b8c\u5168\u5e73\u65b9\u5f0f(3x-4)^2;\uff0c\u53f3\u8fb9=11>0\uff0c\u6240\u4ee5\u6b64\u65b9\u7a0b\u4e5f\u53ef\u7528\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\u89e3\u3002 \u3000\u3000\uff081\uff09\u89e3\uff1a(3x+1)^2=7 \u3000\u3000\u2234(3x+1)^2=7 \u3000\u3000\u22343x+1=\u00b1\u221a7(\u6ce8\u610f\u4e0d\u8981\u4e22\u89e3) \u3000\u3000\u2234x= \ufe59\ufe631\u00b1\u221a7\ufe5a/3 \u3000\u3000\u2234\u539f\u65b9\u7a0b\u7684\u89e3\u4e3ax?=\ufe59\u221a7\ufe631\ufe5a/3,x?=\ufe59\ufe63\u221a7-1\ufe5a/3 \u3000\u3000\uff082\uff09\u89e3\uff1a 9x^2-24x+16=11 \u3000\u3000\u2234(3x-4)^2=11 \u3000\u3000\u22343x-4=\u00b1\u221a11 \u3000\u3000\u2234x=\ufe59 4\u00b1\u221a11\ufe5a/3 \u3000\u3000\u2234\u539f\u65b9\u7a0b\u7684\u89e3\u4e3ax?=\ufe594\ufe62\u221a11\ufe5a/3,x?= \ufe594\ufe63\u221a11\ufe5a/3 \u3000\u30002\uff0e\u914d\u65b9\u6cd5\uff1a\u7528\u914d\u65b9\u6cd5\u89e3\u65b9\u7a0bax^2+bx+c=0 (a\u22600) \u3000\u3000\u5148\u5c06\u5e38\u6570c\u79fb\u5230\u65b9\u7a0b\u53f3\u8fb9\uff1aax^2+bx=-c \u3000\u3000\u5c06\u4e8c\u6b21\u9879\u7cfb\u6570\u5316\u4e3a1\uff1ax^2+b/ax=- c/a \u3000\u3000\u65b9\u7a0b\u4e24\u8fb9\u5206\u522b\u52a0\u4e0a\u4e00\u6b21\u9879\u7cfb\u6570\u7684\u4e00\u534a\u7684\u5e73\u65b9\uff1ax^2+b/ax+( b/2a)^2=- c/a+( b/2a)^2; \u3000\u3000\u65b9\u7a0b\u5de6\u8fb9\u6210\u4e3a\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff1a(x+b/2a )2= -c/a\ufe62\ufe59b/2a\ufe5a² \u3000\u3000\u5f53b²-4ac\u22650\u65f6\uff0cx+b/2a =\u00b1\u221a\ufe59\ufe63c/a\ufe5a\ufe62\ufe59b/2a\ufe5a² \u3000\u3000\u2234x=\ufe5b\ufe63b\u00b1[\u221a\ufe59b²\ufe634ac\ufe5a]\ufe5c/2a(\u8fd9\u5c31\u662f\u6c42\u6839\u516c\u5f0f) \u3000\u3000\u4f8b2\uff0e\u7528\u914d\u65b9\u6cd5\u89e3\u65b9\u7a0b 3x²-4x-2=0 \u3000\u3000\u89e3\uff1a\u5c06\u5e38\u6570\u9879\u79fb\u5230\u65b9\u7a0b\u53f3\u8fb9 3x²-4x=2 \u3000\u3000\u5c06\u4e8c\u6b21\u9879\u7cfb\u6570\u5316\u4e3a1\uff1ax²-\ufe594/3\ufe5ax= ? \u3000\u3000\u65b9\u7a0b\u4e24\u8fb9\u90fd\u52a0\u4e0a\u4e00\u6b21\u9879\u7cfb\u6570\u4e00\u534a\u7684\u5e73\u65b9\uff1ax²-\ufe594/3\ufe5ax+( 4/6)²=? +(4/6 )² \u3000\u3000\u914d\u65b9\uff1a(x-4/6)²= ? +(4/6 )² \u3000\u3000\u76f4\u63a5\u5f00\u5e73\u65b9\u5f97\uff1ax-4/6=\u00b1 \u221a[? +(4/6 )² ] \u3000\u3000\u2234x= 4/6\u00b1 \u221a[? +(4/6 )² ] \u3000\u3000\u2234\u539f\u65b9\u7a0b\u7684\u89e3\u4e3ax?=4/6\ufe62\u221a\ufe5910/6\ufe5a,x?=4/6\ufe63\u221a\ufe5910/6\ufe5a . \u3000\u30003\uff0e\u516c\u5f0f\u6cd5\uff1a\u628a\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u5316\u6210\u4e00\u822c\u5f62\u5f0f\uff0c\u7136\u540e\u8ba1\u7b97\u5224\u522b\u5f0f\u25b3=b²-4ac\u7684\u503c\uff0c\u5f53b²-4ac\u22650\u65f6\uff0c\u628a\u5404\u9879\u7cfb\u6570a, b, c\u7684\u503c\u4ee3\u5165\u6c42\u6839\u516c\u5f0fx=[-b\u00b1\u221a(b²-4ac)]/(2a) , (b²-4ac\u22650)\u5c31\u53ef\u5f97\u5230\u65b9\u7a0b\u7684\u6839\u3002 \u3000\u3000\u4f8b3\uff0e\u7528\u516c\u5f0f\u6cd5\u89e3\u65b9\u7a0b 2x²-8x=-5 \u3000\u3000\u89e3\uff1a\u5c06\u65b9\u7a0b\u5316\u4e3a\u4e00\u822c\u5f62\u5f0f\uff1a2x²-8x+5=0 \u3000\u3000\u2234a=2, b=-8, c=5 \u3000\u3000b²-4ac=(-8)²-4\u00d72\u00d75=64-40=24>0 \u3000\u3000\u2234x=[(-b\u00b1\u221a(b²-4ac)]/(2a) \u3000\u3000\u2234\u539f\u65b9\u7a0b\u7684\u89e3\u4e3ax?=,x?= . \u3000\u30004\uff0e\u56e0\u5f0f\u5206\u89e3\u6cd5\uff1a\u628a\u65b9\u7a0b\u53d8\u5f62\u4e3a\u4e00\u8fb9\u662f\u96f6\uff0c\u628a\u53e6\u4e00\u8fb9\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u5206\u89e3\u6210\u4e24\u4e2a\u4e00\u6b21\u56e0\u5f0f\u7684\u79ef\u7684\u5f62\u5f0f\uff0c\u8ba9\u4e24\u4e2a\u4e00\u6b21\u56e0\u5f0f\u5206\u522b\u7b49\u4e8e\u96f6\uff0c\u5f97\u5230\u4e24\u4e2a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\uff0c\u89e3\u8fd9\u4e24\u4e2a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6240\u5f97\u5230\u7684\u6839\uff0c\u5c31\u662f\u539f\u65b9\u7a0b\u7684\u4e24\u4e2a\u6839\u3002\u8fd9\u79cd\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u65b9\u6cd5\u53eb\u505a\u56e0\u5f0f\u5206\u89e3\u6cd5\u3002 \u3000\u3000\u4f8b4\uff0e\u7528\u56e0\u5f0f\u5206\u89e3\u6cd5\u89e3\u4e0b\u5217\u65b9\u7a0b\uff1a \u3000\u3000(1) (x+3)(x-6)=-8 (2) 2x²+3x=0 \u3000\u3000(3) 6x²+5x-50=0 (\u9009\u5b66\uff09 (4)x2-2( + )x+4=0 \uff08\u9009\u5b66\uff09 \u3000\u3000(1)\u89e3\uff1a(x+3)(x-6)=-8 \u5316\u7b80\u6574\u7406\u5f97 \u3000\u3000x2-3x-10=0 (\u65b9\u7a0b\u5de6\u8fb9\u4e3a\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u53f3\u8fb9\u4e3a\u96f6) \u3000\u3000(x-5)(x+2)=0 (\u65b9\u7a0b\u5de6\u8fb9\u5206\u89e3\u56e0\u5f0f) \u3000\u3000\u2234x-5=0\u6216x+2=0 (\u8f6c\u5316\u6210\u4e24\u4e2a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b) \u3000\u3000\u2234x1=5,x2=-2\u662f\u539f\u65b9\u7a0b\u7684\u89e3\u3002 \u3000\u3000(2)\u89e3\uff1a2x2+3x=0 \u3000\u3000x(2x+3)=0 (\u7528\u63d0\u516c\u56e0\u5f0f\u6cd5\u5c06\u65b9\u7a0b\u5de6\u8fb9\u5206\u89e3\u56e0\u5f0f) \u3000\u3000\u2234x=0\u62162x+3=0 (\u8f6c\u5316\u6210\u4e24\u4e2a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b) \u3000\u3000\u2234x1=0\uff0cx2=-\u662f\u539f\u65b9\u7a0b\u7684\u89e3\u3002 \u3000\u3000\u6ce8\u610f\uff1a\u6709\u4e9b\u540c\u5b66\u505a\u8fd9\u79cd\u9898\u76ee\u65f6\u5bb9\u6613\u4e22\u6389x=0\u8fd9\u4e2a\u89e3\uff0c\u5e94\u8bb0\u4f4f\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u6709\u4e24\u4e2a\u89e3\u3002 \u3000\u3000(3)\u89e3\uff1a6x2+5x-50=0 \u3000\u3000(2x-5)(3x+10)=0 (\u5341\u5b57\u76f8\u4e58\u5206\u89e3\u56e0\u5f0f\u65f6\u8981\u7279\u522b\u6ce8\u610f\u7b26\u53f7\u4e0d\u8981\u51fa\u9519) \u3000\u3000\u22342x-5=0\u62163x+10=0 \u3000\u3000\u2234x1=, x2=- \u662f\u539f\u65b9\u7a0b\u7684\u89e3\u3002 \u3000\u3000(4)\u89e3\uff1ax2-2(+ )x+4 =0 \uff08\u22354 \u53ef\u5206\u89e3\u4e3a2 \u00b72 \uff0c\u2234\u6b64\u9898\u53ef\u7528\u56e0\u5f0f\u5206\u89e3\u6cd5\uff09 \u3000\u3000(x-2)(x-2 )=0 \u3000\u3000\u2234x1=2 ,x2=2\u662f\u539f\u65b9\u7a0b\u7684\u89e3\u3002 \u3000\u3000\u5c0f\u7ed3\uff1a \u3000\u3000\u4e00\u822c\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\uff0c\u6700\u5e38\u7528\u7684\u65b9\u6cd5\u8fd8\u662f\u56e0\u5f0f\u5206\u89e3\u6cd5\uff0c\u5728\u5e94\u7528\u56e0\u5f0f\u5206\u89e3\u6cd5\u65f6\uff0c\u4e00\u822c\u8981\u5148\u5c06\u65b9\u7a0b\u5199\u6210\u4e00\u822c\u5f62\u5f0f\uff0c\u540c\u65f6\u5e94\u4f7f\u4e8c\u6b21\u9879\u7cfb\u6570\u5316\u4e3a\u6b63\u6570\u3002 \u3000\u3000\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\u662f\u6700\u57fa\u672c\u7684\u65b9\u6cd5\u3002 \u3000\u3000\u516c\u5f0f\u6cd5\u548c\u914d\u65b9\u6cd5\u662f\u6700\u91cd\u8981\u7684\u65b9\u6cd5\u3002\u516c\u5f0f\u6cd5\u9002\u7528\u4e8e\u4efb\u4f55\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\uff08\u6709\u4eba\u79f0\u4e4b\u4e3a\u4e07\u80fd\u6cd5\uff09\uff0c\u5728\u4f7f\u7528\u516c\u5f0f\u6cd5\u65f6\uff0c\u4e00\u5b9a\u8981\u628a\u539f\u65b9\u7a0b\u5316\u6210\u4e00\u822c\u5f62\u5f0f\uff0c\u4ee5\u4fbf\u786e\u5b9a\u7cfb\u6570\uff0c\u800c\u4e14\u5728\u7528\u516c\u5f0f\u524d\u5e94\u5148\u8ba1\u7b97\u5224\u522b\u5f0f\u7684\u503c\uff0c\u4ee5\u4fbf\u5224\u65ad\u65b9\u7a0b\u662f\u5426\u6709\u89e3\u3002 \u3000\u3000\u914d\u65b9\u6cd5\u662f\u63a8\u5bfc\u516c\u5f0f\u7684\u5de5\u5177\uff0c\u638c\u63e1\u516c\u5f0f\u6cd5\u540e\u5c31\u53ef\u4ee5\u76f4\u63a5\u7528\u516c\u5f0f\u6cd5\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u4e86\uff0c\u6240\u4ee5\u4e00\u822c\u4e0d\u7528\u914d\u65b9\u6cd5 \u3000\u3000\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u3002\u4f46\u662f\uff0c\u914d\u65b9\u6cd5\u5728\u5b66\u4e60\u5176\u4ed6\u6570\u5b66\u77e5\u8bc6\u65f6\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u662f\u521d\u4e2d\u8981\u6c42\u638c\u63e1\u7684\u4e09\u79cd\u91cd\u8981\u7684\u6570\u5b66\u65b9\u6cd5\u4e4b\u4e00\uff0c\u4e00\u5b9a\u8981\u638c\u63e1\u597d\u3002\uff08\u4e09\u79cd\u91cd\u8981\u7684\u6570\u5b66\u65b9\u6cd5\uff1a\u6362\u5143\u6cd5\uff0c\u914d\u65b9\u6cd5\uff0c\u5f85\u5b9a\u7cfb\u6570\u6cd5\uff09\u3002 \u3000\u3000\u4f8b5\uff0e\u7528\u9002\u5f53\u7684\u65b9\u6cd5\u89e3\u4e0b\u5217\u65b9\u7a0b\u3002(\u9009\u5b66\uff09 \u3000\u3000\uff081\uff094(x+2)2-9(x-3)2=0 \uff082\uff09x2+(2-)x+ -3=0 \u3000\u3000\uff083\uff09 x2-2 x=- \uff084\uff094x2-4mx-10x+m2+5m+6=0 \u3000\u3000\u5206\u6790\uff1a\uff081\uff09\u9996\u5148\u5e94\u89c2\u5bdf\u9898\u76ee\u6709\u65e0\u7279\u70b9\uff0c\u4e0d\u8981\u76f2\u76ee\u5730\u5148\u505a\u4e58\u6cd5\u8fd0\u7b97\u3002\u89c2\u5bdf\u540e\u53d1\u73b0\uff0c\u65b9\u7a0b\u5de6\u8fb9\u53ef\u7528\u5e73\u65b9\u5dee\u516c\u5f0f\u5206\u89e3\u56e0\u5f0f\uff0c\u5316\u6210\u4e24\u4e2a\u4e00\u6b21\u56e0\u5f0f\u7684\u4e58\u79ef\u3002 \u3000\u3000\uff082\uff09\u53ef\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5c06\u65b9\u7a0b\u5de6\u8fb9\u56e0\u5f0f\u5206\u89e3\u3002 \u3000\u3000\uff083\uff09\u5316\u6210\u4e00\u822c\u5f62\u5f0f\u540e\u5229\u7528\u516c\u5f0f\u6cd5\u89e3\u3002 \u3000\u3000\uff084\uff09\u628a\u65b9\u7a0b\u53d8\u5f62\u4e3a 4x2-2(2m+5)x+(m+2)(m+3)=0\uff0c\u7136\u540e\u53ef\u5229\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u56e0\u5f0f\u5206\u89e3\u3002 \u3000\u3000\uff081\uff09\u89e3\uff1a4(x+2)2-9(x-3)2=0 \u3000\u3000[2(x+2)+3(x-3)][2(x+2)-3(x-3)]=0 \u3000\u3000(5x-5)(-x+13)=0 \u3000\u30005x-5=0\u6216-x+13=0 \u3000\u3000\u2234x1=1,x2=13 \u3000\u3000\uff082\uff09\u89e3\uff1a x2+(2- )x+ -3=0 \u3000\u3000[x-(-3)](x-1)=0 \u3000\u3000x-(-3)=0\u6216x-1=0 \u3000\u3000\u2234x1=-3\uff0cx2=1 \u3000\u3000\uff083\uff09\u89e3\uff1ax2-2 x=- \u3000\u3000x2-2 x+ =0 (\u5148\u5316\u6210\u4e00\u822c\u5f62\u5f0f) \u3000\u3000\u25b3=(-2 )2-4 \u00d7=12-8=4>0 \u3000\u3000\u2234x= \u3000\u3000\u2234x1=,x2= \u3000\u3000\uff084\uff09\u89e3\uff1a4x2-4mx-10x+m2+5m+6=0 \u3000\u30004x2-2(2m+5)x+(m+2)(m+3)=0 \u3000\u3000[2x-(m+2)][2x-(m+3)]=0 \u3000\u30002x-(m+2)=0\u62162x-(m+3)=0 \u3000\u3000\u2234x1= ,x2= \u3000\u3000\u4f8b6\uff0e\u6c42\u65b9\u7a0b3(x+1)2+5(x+1)(x-4)+2(x-4)2=0\u7684\u4e8c\u6839\u3002 (\u9009\u5b66\uff09 \u3000\u3000\u5206\u6790\uff1a\u6b64\u65b9\u7a0b\u5982\u679c\u5148\u505a\u4e58\u65b9\uff0c\u4e58\u6cd5\uff0c\u5408\u5e76\u540c\u7c7b\u9879\u5316\u6210\u4e00\u822c\u5f62\u5f0f\u540e\u518d\u505a\u5c06\u4f1a\u6bd4\u8f83\u7e41\u7410\uff0c\u4ed4\u7ec6\u89c2\u5bdf\u9898\u76ee\uff0c\u6211\u4eec\u53d1\u73b0\u5982\u679c\u628ax+1\u548cx-4\u5206\u522b\u770b\u4f5c\u4e00\u4e2a\u6574\u4f53\uff0c\u5219\u65b9\u7a0b\u5de6\u8fb9\u53ef\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\uff08\u5b9e\u9645\u4e0a\u662f\u8fd0\u7528\u6362\u5143\u7684\u65b9\u6cd5\uff09 \u3000\u3000\u89e3\uff1a[3(x+1)+2(x-4)][(x+1)+(x-4)]=0 \u3000\u3000\u5373 (5x-5)(2x-3)=0 \u3000\u3000\u22345(x-1)(2x-3)=0 \u3000\u3000(x-1)(2x-3)=0 \u3000\u3000\u2234x-1=0\u62162x-3=0 \u3000\u3000\u2234x1=1,x2=\u662f\u539f\u65b9\u7a0b\u7684\u89e3\u3002 \u3000\u3000\u4f8b7\uff0e\u7528\u914d\u65b9\u6cd5\u89e3\u5173\u4e8ex\u7684\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0bx2+px+q=0 \u3000\u3000\u89e3\uff1ax2+px+q=0\u53ef\u53d8\u5f62\u4e3a \u3000\u3000x2+px=-q (\u5e38\u6570\u9879\u79fb\u5230\u65b9\u7a0b\u53f3\u8fb9) \u3000\u3000x2+px+( )2=-q+()2 (\u65b9\u7a0b\u4e24\u8fb9\u90fd\u52a0\u4e0a\u4e00\u6b21\u9879\u7cfb\u6570\u4e00\u534a\u7684\u5e73\u65b9) \u3000\u3000(x+)2= (\u914d\u65b9) \u3000\u3000\u5f53p2-4q\u22650\u65f6\uff0c\u22650\uff08\u5fc5\u987b\u5bf9p2-4q\u8fdb\u884c\u5206\u7c7b\u8ba8\u8bba\uff09 \u3000\u3000\u2234x=- \u00b1= \u3000\u3000\u2234x1= ,x2= \u3000\u3000\u5f53p2-4q<0\u65f6\uff0c<0\u6b64\u65f6\u539f\u65b9\u7a0b\u65e0\u5b9e\u6839\u3002 \u3000\u3000\u8bf4\u660e\uff1a\u672c\u9898\u662f\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b\uff0c\u9898\u76ee\u4e2d\u5bf9p, q\u6ca1\u6709\u9644\u52a0\u6761\u4ef6\uff0c\u56e0\u6b64\u5728\u89e3\u9898\u8fc7\u7a0b\u4e2d\u5e94\u968f\u65f6\u6ce8\u610f\u5bf9\u5b57\u6bcd\u53d6\u503c\u7684\u8981\u6c42\uff0c\u5fc5\u8981\u65f6\u8fdb\u884c\u5206\u7c7b\u8ba8\u8bba\u3002 \u3000\u3000\u7ec3\u4e60\uff1a \u3000\u3000\uff08\u4e00\uff09\u7528\u9002\u5f53\u7684\u65b9\u6cd5\u89e3\u4e0b\u5217\u65b9\u7a0b\uff1a \u3000\u30001. 6x2-x-2=0 2. (x+5)(x-5)=3 \u3000\u30003. x2-x=0 4. x2-4x+4=0 \u3000\u30005. 3x2+1=2x 6. (2x+3)2+5(2x+3)-6=0 \u3000\u3000\uff08\u4e8c\uff09\u89e3\u4e0b\u5217\u5173\u4e8ex\u7684\u65b9\u7a0b \u3000\u30001.x2-ax+-b2=0 2. x2-( + )ax+ a2=0 \u3000\u3000\u7ec3\u4e60\u53c2\u8003\u7b54\u6848\uff1a \u3000\u3000\uff08\u4e00\uff091.x1=- ,x2= 2.x1=2,x2=-2 \u3000\u30003.x1=0,x2= 4.x1=x2=2 5.x1=x2= \u3000\u30006.\u89e3\uff1a\uff08\u628a2x+3\u770b\u4f5c\u4e00\u4e2a\u6574\u4f53\uff0c\u5c06\u65b9\u7a0b\u5de6\u8fb9\u5206\u89e3\u56e0\u5f0f\uff09 \u3000\u3000[(2x+3)+6][(2x+3)-1]=0 \u3000\u3000\u5373 (2x+9)(2x+2)=0 \u3000\u3000\u22342x+9=0\u62162x+2=0 \u3000\u3000\u2234x1=-,x2=-1\u662f\u539f\u65b9\u7a0b\u7684\u89e3\u3002 \u3000\u3000\uff08\u4e8c\uff091\uff0e\u89e3\uff1ax2-ax+( +b)( -b)=0 2\u3001\u89e3\uff1ax2-(+ )ax+ a\u00b7 a=0 \u3000\u3000[x-( +b)] [x-( -b)]=0 (x- a)(x-a)=0 \u3000\u3000\u2234x-( +b)=0\u6216x-( -b) =0 x- a=0\u6216x-a=0 \u3000\u3000\u2234x1= +b\uff0cx2= -b\u662f \u2234x1= a\uff0cx2=a\u662f \u3000\u3000\u539f\u65b9\u7a0b\u7684\u89e3\u3002 \u539f\u65b9\u7a0b\u7684\u89e3\u3002 \u3000\u3000\u6d4b\u8bd5 \u3000\u3000\u9009\u62e9\u9898 \u3000\u30001\uff0e\u65b9\u7a0bx(x-5)=5(x-5)\u7684\u6839\u662f\uff08 \uff09 \u3000\u3000A\u3001x=5 B\u3001x=-5 C\u3001x1=x2=5 D\u3001x1=x2=-5 \u3000\u30002\uff0e\u591a\u9879\u5f0fa2+4a-10\u7684\u503c\u7b49\u4e8e11\uff0c\u5219a\u7684\u503c\u4e3a\uff08 \uff09\u3002 \u3000\u3000A\u30013\u62167 B\u3001-3\u62167 C\u30013\u6216-7 D\u3001-3\u6216-7 \u3000\u30003\uff0e\u82e5\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0bax2+bx+c=0\u4e2d\u7684\u4e8c\u6b21\u9879\u7cfb\u6570\uff0c\u4e00\u6b21\u9879\u7cfb\u6570\u548c\u5e38\u6570\u9879\u4e4b\u548c\u7b49\u4e8e\u96f6\uff0c\u90a3\u4e48\u65b9\u7a0b\u5fc5\u6709\u4e00\u4e2a\u6839\u662f\uff08 \uff09\u3002 \u3000\u3000A\u30010 B\u30011 C\u3001-1 D\u3001\u00b11 \u3000\u30004\uff0e \u4e00\u5143\u4e8c\u6b21\u65b9\u7a0bax2+bx+c=0\u6709\u4e00\u4e2a\u6839\u662f\u96f6\u7684\u6761\u4ef6\u4e3a\uff08 \uff09\u3002 \u3000\u3000A\u3001b\u22600\u4e14c=0 B\u3001b=0\u4e14c\u22600 \u3000\u3000C\u3001b=0\u4e14c=0 D\u3001c=0 \u3000\u30005\uff0e \u65b9\u7a0bx2-3x=10\u7684\u4e24\u4e2a\u6839\u662f\uff08 \uff09\u3002 \u3000\u3000A\u3001-2\uff0c5 B\u30012\uff0c-5 C\u30012\uff0c5 D\u3001-2\uff0c-5 \u3000\u30006\uff0e \u65b9\u7a0bx2-3x+3=0\u7684\u89e3\u662f\uff08 \uff09\u3002 \u3000\u3000A\u3001 B\u3001 C\u3001 D\u3001\u65e0\u5b9e\u6839 \u3000\u30007\uff0e \u65b9\u7a0b2x2-0.15=0\u7684\u89e3\u662f\uff08 \uff09\u3002 \u3000\u3000A\u3001x= B\u3001x=- \u3000\u3000C\u3001x1=0.27, x2=-0.27 D\u3001x1=, x2=- \u3000\u30008\uff0e \u65b9\u7a0bx2-x-4=0\u5de6\u8fb9\u914d\u6210\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\u540e\uff0c\u6240\u5f97\u7684\u65b9\u7a0b\u662f\uff08 \uff09\u3002 \u3000\u3000A\u3001(x-)2= B\u3001(x- )2=- \u3000\u3000C\u3001(x- )2= D\u3001\u4ee5\u4e0a\u7b54\u6848\u90fd\u4e0d\u5bf9 \u3000\u30009\uff0e \u5df2\u77e5\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0bx2-2x-m=0\uff0c\u7528\u914d\u65b9\u6cd5\u89e3\u8be5\u65b9\u7a0b\u914d\u65b9\u540e\u7684\u65b9\u7a0b\u662f\uff08 \uff09\u3002 \u3000\u3000A\u3001(x-1)2=m2+1 B\u3001(x-1)2=m-1 C\u3001(x-1)2=1-m D\u3001(x-1)2=m+1 \u3000\u3000\u7b54\u6848\u4e0e\u89e3\u6790 \u3000\u3000\u7b54\u6848\uff1a1.C 2.C 3.B 4.D 5.A 6.D 7.D 8.C 9.D \u3000\u3000\u89e3\u6790\uff1a \u3000\u30001\uff0e\u5206\u6790\uff1a\u79fb\u9879\u5f97\uff1a(x-5)2=0\uff0c\u5219x1=x2=5, \u3000\u3000\u6ce8\u610f\uff1a\u65b9\u7a0b\u4e24\u8fb9\u4e0d\u8981\u8f7b\u6613\u9664\u4ee5\u4e00\u4e2a\u6574\u5f0f\uff0c\u53e6\u5916\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u6709\u5b9e\u6570\u6839\uff0c\u4e00\u5b9a\u662f\u4e24\u4e2a\u3002 \u3000\u30002\uff0e\u5206\u6790\uff1a\u4f9d\u9898\u610f\u5f97\uff1aa2+4a-10=11, \u89e3\u5f97 a=3\u6216a=-7. \u3000\u30003\uff0e\u5206\u6790\uff1a\u4f9d\u9898\u610f\uff1a\u6709a+b+c=0, \u65b9\u7a0b\u5de6\u4fa7\u4e3aa+b+c, \u4e14\u5177\u4ec5\u6709x=1\u65f6\uff0c ax2+bx+c=a+b+c\uff0c\u610f\u5473\u7740\u5f53x=1\u65f6\uff0c\u65b9\u7a0b\u6210\u7acb\uff0c\u5219\u5fc5\u6709\u6839\u4e3ax=1\u3002 \u3000\u30004\uff0e\u5206\u6790\uff1a\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b ax2+bx+c=0\u82e5\u6709\u4e00\u4e2a\u6839\u4e3a\u96f6\uff0c \u3000\u3000\u5219ax2+bx+c\u5fc5\u5b58\u5728\u56e0\u5f0fx\uff0c\u5219\u6709\u4e14\u4ec5\u6709c=0\u65f6\uff0c\u5b58\u5728\u516c\u56e0\u5f0fx\uff0c\u6240\u4ee5 c=0. \u3000\u3000\u53e6\u5916\uff0c\u8fd8\u53ef\u4ee5\u5c06x=0\u4ee3\u5165\uff0c\u5f97c=0\uff0c\u66f4\u7b80\u5355\uff01 \u3000\u30005\uff0e\u5206\u6790\uff1a\u539f\u65b9\u7a0b\u53d8\u4e3a x²-3x-10=0, \u3000\u3000\u5219(x-5)(x+2)=0 \u3000\u3000x-5=0 \u6216x+2=0 \u3000\u3000x1=5, x2=-2. \u3000\u30006\uff0e\u5206\u6790\uff1a\u0394=9-4\u00d73=-3<0\uff0c\u5219\u539f\u65b9\u7a0b\u65e0\u5b9e\u6839\u3002 \u3000\u30007\uff0e\u5206\u6790\uff1a2x²=0.15 \u3000\u3000x2= \u3000\u3000x=\u00b1 \u3000\u3000\u6ce8\u610f\u6839\u5f0f\u7684\u5316\u7b80\uff0c\u5e76\u6ce8\u610f\u76f4\u63a5\u5f00\u5e73\u65b9\u65f6\uff0c\u4e0d\u8981\u4e22\u6839\u3002 \u3000\u30008\uff0e\u5206\u6790\uff1a\u4e24\u8fb9\u4e58\u4ee53\u5f97\uff1ax2-3x-12=0\uff0c\u7136\u540e\u6309\u7167\u4e00\u6b21\u9879\u7cfb\u6570\u914d\u65b9\uff0cx2-3x+(-)2=12+(- )2\uff0c \u3000\u3000\u6574\u7406\u4e3a\uff1a(x-)2= \u3000\u3000\u65b9\u7a0b\u53ef\u4ee5\u5229\u7528\u7b49\u5f0f\u6027\u8d28\u53d8\u5f62\uff0c\u5e76\u4e14 x2-bx\u914d\u65b9\u65f6\uff0c\u914d\u65b9\u9879\u4e3a\u4e00\u6b21\u9879\u7cfb\u6570-b\u7684\u4e00\u534a\u7684\u5e73\u65b9\u3002 \u3000\u30009\uff0e\u5206\u6790\uff1ax2-2x=m, \u5219 x2-2x+1=m+1 \u3000\u3000\u5219(x-1)2=m+1.
\u89e3\u65b9\u7a0b\u7684\u6b65\u9aa4 \uff081\uff09\u6709\u62ec\u53f7\u5c31\u5148\u53bb\u6389 \uff082\uff09\u79fb\u9879\uff1a\u5c06\u542b\u672a\u77e5\u6570\u7684\u9879\u79fb\u5230\u5de6\u8fb9\uff0c\u5e38\u6570\u9879\u79fb\u5230\u53e6\u53f3\u8fb9 \uff083\uff09\u5408\u5e76\u540c\u7c7b\u9879\uff1a\u4f7f\u65b9\u7a0b\u53d8\u5f62\u4e3a\u5355\u9879\u5f0f \uff084\uff09\u65b9\u7a0b\u4e24\u8fb9\u540c\u65f6\u9664\u4ee5\u672a\u77e5\u6570\u7684\u7cfb\u6570\u5f97\u672a\u77e5\u6570\u7684\u503c \u4f8b\u5982\uff1a 3+x=18 \u89e3: x =18-3 x =15 \u2234x=15\u662f\u65b9\u7a0b\u7684\u89e3 \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014 4x+2\uff0879-x\uff09=192 \u89e3\uff1a4x+158-2x=192 4x-2x+158=192 2x+158=192 2x=192-158 2x=34 x=17 \u2234x=17\u662f\u65b9\u7a0b\u7684\u89e3 \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014 \u03c0r=6.28\uff08\u53ea\u53d6\u03c0\u5c0f\u6570\u70b9\u540e\u4e24\u4f4d\uff09 \u89e3\u8fd9\u9053\u9898\u9996\u5148\u8981\u77e5\u9053\u03c0\u7b49\u4e8e\u51e0\uff0c\u03c0=3.1415926535\uff0c\u53ea\u53d63.14\uff0c \u89e3\uff1a3.14r=6.28 r=6.28/3.14=2 \u4e0d\u8fc7\uff0cx\u4e0d\u4e00\u5b9a\u653e\u5728\u65b9\u7a0b\u5de6\u8fb9\uff0c\u6216\u4e00\u4e2a\u65b9\u7a0b\u5f0f\u5b50\u91cc\u6709\u4e24\u4e2ax\uff0c\u8fd9\u6837\u5c31\u8981\u7528\u6570\u5b66\u4e2d\u7684\u7b80\u4fbf\u8ba1\u7b97\u65b9\u6cd5\u53bb\u89e3\u51b3\u5b83\u4e86\u3002\u6709\u4e9b\u5f0f\u5b50\u53f3\u8fb9\u6709x,\u4e3a\u4e86\u7b80\u4fbf\u7b97,\u53ef\u4ee5\u8c03\u6362\u4f4d\u7f6e\u3002
\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b
\u4eba\u6559\u72485\u5e74\u7ea7\u6570\u5b66\u4e0a\u518c\u7b2c\u56db\u7ae0\u4f1a\u5b66\u5230\uff0c\u5180\u6559\u72487\u5e74\u7ea7\u6570\u5b66\u4e0b\u518c\u7b2c\u4e03\u7ae0\u4f1a\u5b66\u5230,\u82cf\u6559\u72485\u5e74\u7ea7\u4e0b\u7b2c\u4e00\u7ae0
\u5b9a\u4e49\uff1a\u53ea\u542b\u6709\u4e00\u4e2a\u672a\u77e5\u6570,\u4e14\u672a\u77e5\u6570\u6b21\u6570\u662f\u4e00\u7684\u6574\u5f0f\u65b9\u7a0b\u53eb\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u3002\u901a\u5e38\u5f62\u5f0f\u662fkx+b=0(k\uff0cb\u4e3a\u5e38\u6570\uff0c\u4e14k\u22600\uff09\u3002
\u4e00\u822c\u89e3\u6cd5\uff1a
\u2488\u53bb\u5206\u6bcd \u65b9\u7a0b\u4e24\u8fb9\u540c\u65f6\u4e58\u5404\u5206\u6bcd\u7684\u6700\u5c0f\u516c\u500d\u6570\u3002
\u2489\u53bb\u62ec\u53f7 \u4e00\u822c\u5148\u53bb\u5c0f\u62ec\u53f7\uff0c\u518d\u53bb\u4e2d\u62ec\u53f7\uff0c\u6700\u540e\u53bb\u5927\u62ec\u53f7\u3002\u4f46\u987a\u5e8f\u6709\u65f6\u53ef\u4f9d\u636e\u60c5\u51b5\u800c\u5b9a\u4f7f\u8ba1\u7b97\u7b80\u4fbf\u3002\u53ef\u6839\u636e\u4e58\u6cd5\u5206\u914d\u5f8b\u3002
\u248a\u79fb\u9879 \u628a\u65b9\u7a0b\u4e2d\u542b\u6709\u672a\u77e5\u6570\u7684\u9879\u79fb\u5230\u65b9\u7a0b\u7684\u53e6\u4e00\u8fb9\uff0c\u5176\u4f59\u5404\u9879\u79fb\u5230\u65b9\u7a0b\u7684\u53e6\u4e00\u8fb9\u79fb\u9879\u65f6\u522b\u5fd8\u8bb0\u4e86\u8981\u53d8\u53f7\u3002
\u248b\u5408\u5e76\u540c\u7c7b\u9879 \u5c06\u539f\u65b9\u7a0b\u5316\u4e3aax=b(a\u22600)\u7684\u5f62\u5f0f\u3002
\u248c\u7cfb\u6570\u5316\u4e00 \u65b9\u7a0b\u4e24\u8fb9\u540c\u65f6\u9664\u4ee5\u672a\u77e5\u6570\u7684\u7cfb\u6570\u3002
\u248d\u5f97\u51fa\u65b9\u7a0b\u7684\u89e3\u3002
\u7f51\u9875\u4e0aCOPY\u7684\uff0c\u6162\u6162\u770b\u5427
a=umg/k, b=uh
方程化为(t-h)(x+b)/t=a
(t-h)(x+b)=at
(x+b-a)t=h(x+b)
平方：(x+b-a)^2(h^2+x^2)=h^2(x+b)^2
a^2(h^2+x^2)+x^2(x+b)^2-2a(x+b)(h^2+x^2)=0
a^2h^2+a^2x^2+x^4+2bx^3+b^2x^2-2a(h^2x+x^3+bh^2+bx^2)=0
x^4+x^3(2b-2a)+x^2(a^2+b^2-2ab)-2ah^2x+a^2h^2-2abh^2=0
x^4+2(b-a)x^3+(a-b)^2x^2-2ah^2x+ah^2(a-2b)=0
这就化成了一元四次方程，可以用4次方程的求根公式来解。
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