用适当方法解下列方程:(1)(x+6) 2 -9=0(2)x 2 +17=8x(3)x(2x-5)=4x-10

2024-12-03 23:17:59
推荐回答(1个)
回答1:

(1)(x+6) 2 -9=0,
(x+6+3)(x+6-3)=0,
x+6+3=0,x+6-3=0,
x 1 =-9,x 2 =-3;

(2)x 2 +17=8x,
x 2 -8x=-17,
配方得:x 2 -8x+4 2 =-17+4 2
即(x-4) 2 =-1,
∵不论x为何值,x-4的平方都不等于-1,
∴此方程无解;

(3)x(2x-5)=4x-10,
x(2x-5)-2(2x-5)=0,
(2x-5)(x-2)=0,
2x-5=0,x-2=0,
解得:x 1 =
5
2
,x 2 =2.