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用配方法解下列方程①x2-2x=2x+1②y2-4√3y+12=0③2x2+1=3x④﹙x-3﹚﹙2x+1﹚=-5
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用配方法解下列方程①x2-2x=2x+1②y2-4√3y+12=0③2x2+1=3x④﹙x-3﹚﹙2x+1﹚=-5
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答案和解析
①x2-2x=2x+1
x²-4x=1;
x²-4x+4=5;
(x-2)²=5;
x-2=±√5;
x=2±√5;
②y2-4√3y+12=0
(y-2√3)²=0;
y=2√3;
③2x2+1=3x
x²-3x/2=-1/2;
(x-3/4)²=-1/2+9/16;
(x-3/4)²=1/16;
x-3/4=±1/4;
x=3/4±1/4;
x=1或x=1/2;
④﹙x-3﹚﹙2x+1﹚=-5
2x²+x-6x-3=-5;
2x²-5x=-2;
x²-5x/2=-1;
(x-5/4)²=-1+25/16;
(x-5/4)²=9/16;
x-5/4=±3/4;
x=5/4±3/4;
x=2或x=1/2;
x²-4x=1;
x²-4x+4=5;
(x-2)²=5;
x-2=±√5;
x=2±√5;
②y2-4√3y+12=0
(y-2√3)²=0;
y=2√3;
③2x2+1=3x
x²-3x/2=-1/2;
(x-3/4)²=-1/2+9/16;
(x-3/4)²=1/16;
x-3/4=±1/4;
x=3/4±1/4;
x=1或x=1/2;
④﹙x-3﹚﹙2x+1﹚=-5
2x²+x-6x-3=-5;
2x²-5x=-2;
x²-5x/2=-1;
(x-5/4)²=-1+25/16;
(x-5/4)²=9/16;
x-5/4=±3/4;
x=5/4±3/4;
x=2或x=1/2;
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