Question

解方程x²-2x+7/(x²-2x)=8

Answer 1

令a=x²-2x

则a+7/a=8

两边乘a

a²-8a+7=0

(a-1)(a-7)=0

a=1,a=7

x²-2x=1

x²-2x-1=0

x=1±√2

x²-2x=7

x²-2x-7=0

x=1±2√2

所以

x=1-√2,x=1+√2,x=1-2√2,x=1+2√2