问题 解答题

解方程:

(1)(x-1)2-4=0

(2)x2-4x-1=0

(3)x2+4x-5=0

(4)x(2x+3)=4x+6.

答案

(1)(x-1)2-4=0,

(x-1+2)(x-1-2)=0,

x-1+2=0,x-1-2=0,

x1=-1,x2=3;

(2)x2-4x-1=0,

x2-4x=1,

配方得:x2-4x+4=1+4,

(x-2)2=5,

开方得:x-2=±

5

x1=2+

5
,x2=2-
5

(3)x2+4x-5=0,

(x+5)(x-1)=0,

x+5=0,x-1=0,

x1=-5,x2=1;

(4)x(2x+3)=4x+6,

x(2x+3)-2(2x+3)=0,

(2x+3)(x-2)=0,

2x+3=0,x-2=0,

x1=-

3
2
,x2=2.

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