Question

用换元法解方程X^2-2X+7/X^2-2X=8，若设X^2-2X=Y,则原方程化为关于Y的整式方程是

Answer 1

将X^2-2X=Y代入X^2-2X+7/X^2-2X=8 得 Y+7/Y=8

Answer 2

y+7/y=8
y^2-8y+7=0
(y-1)(y-7)=0
y=1
y=7
x^2-2x=1,(x-1)^2=2
x-1=±√2
x=1 ±√2
x^2-2x=7,(x-1)^2=8
x-1=±2√2
x=1 ±2√2