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

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