Question

用换元法解方程：2x方-4x+3乘根号（x方-2x+6）=15

Answer 1

2(x^2-2x+6)+3根[x^2-2x+6]=27

设t=根号[x^2-2x+6]>0

则原方程是：2t^2+3t-27=0

(2t+9)(t-3)=0

t=-9/2(不符,舍）

t=3

所以：3=根[ x^2-2x+6]

x^2-2x+6=9

x^2-2x-3=0

[x-3][x+1]=0

x1=3

x2=-1