试题与答案

解下列方程: (1)(2x+5)2-1=0 (2)(x-1)(x+1)=1 (3

题型:解答题

题目:

解下列方程:

(1)(2x+5)2-1=0

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

(3)3(y-1)2=75

(4)x2-2x+1=5

(5)5(x-3)2-125=0

(6)4x2-4x+1=5.

答案:

(1)分解因式得:(2x+5-1)(2x+5+1)=0,

可得2x+4=0或2x+6=0,

解得:x1=-2,x2=-3;

(2)方程整理得:x2=2,

解得:x1=

2
,x2=-
2

(3)方程变形得:(y-1)2=25,

开方得:y-1=5或y-1=-5,

解得:y1=6,y2=-4;

(4)方程变形得:(x-1)2=5,

开方得:x-1=±

5

解得:x1=1+

5
,x2=1-
5

(5)方程变形得:(x-3)2=25,

开方得:x-3=5或x-3=-5,

解得:x1=8,x2=-2;

(6)方程变形得:(2x-1)2=5,

开方得:2x-1=±

5

解得:x1=

1+
5
2
,x2=
1-
5
2

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