搜狗做题网用换元法解分式方程x^2-2x+7/x^2-2x=8
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用换元法解分式方程x^2-2x+7/x^2-2x=8
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答
x^2-2x+7/x^2-2x=8
设y=x^2-2x
则
y+7/y=8
y^2-8y+7=0
(y-7)(y-1)=0
y=7或y=1
x^2-2x=7
x^2-2x-7=0
求根公式得
x=1±2√2
x^2-2x=1
x^2-2x-1=0
求根公式得
x=1±√2
综上
方程解
为x=1±2√2或x=1±√2
x^2-2x+7/x^2-2x=8
设y=x^2-2x
则
y+7/y=8
y^2-8y+7=0
(y-7)(y-1)=0
y=7或y=1
x^2-2x=7
x^2-2x-7=0
求根公式得
x=1±2√2
x^2-2x=1
x^2-2x-1=0
求根公式得
x=1±√2
综上
方程解
为x=1±2√2或x=1±√2
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