选择最佳方法解下列关于x的方程:(1)(x+1) 2 =(1-2x) 2 (2)x 2 -6x+8=0(3) x 2 -2

2025-05-20 20:47:38
推荐回答(1个)
回答1:

(1)(x+1) 2 =(1-2x) 2
开方得:x+1=1-2x或x+1=-(1-2x),
解得:x 1 =2,x 2 =0;
(2)x 2 -6x+8=0,
因式分解得:(x-2)(x-4)=0,
可得x-2=0或x-4=0,
解得:x 1 =2,x 2 =4;
(3)x 2 -2
2
x+2=0,
变形得:x 2 -2
2
+(
2
2 =0,即(x-
2
2 =0,
解得:x 1 =x 2 =
2

(4)x(x+4)=21,
整理得:x 2 +4x-21=0,即(x-3)(x+7)=0,
可得x-3=0或x+7=0,
解得:x 1 =-7,x 2 =3;
(5)-2x 2 +2x+1=0,
这里a=-2,b=2,c=1,
∵△=4+8=12>0,
∴x=
-2±
12
2×(-2)
=
3
2

则x 1 =
1+
3
2
,x 2 =
1-
3
2

(6)x 2 -(2a-b)x+a 2 -ab=0,
因式分解得:(x-a)(x-a+b)=0,
可得x-a=0或x-a+b=0,
解得:x 1 =a,x 2 =a-b.