用换元法解x^2/(x-1)^2-2x/x-1=3
来源:百度知道 编辑:UC知道 时间:2024/06/08 18:52:14
用换元法解x^2/(x-1)^2-2x/x-1=3
用换元法解x^2/(x-1)^2-2x/x-1=3
设y=x/(x-1)
原方程化为y^2-2y-3=0
解得y=3 y=-1
当x/(x-1)=3时 x=3/2
当x/(x-1)=-1时 x=1/2
经检验:x1=3/2 ,x2=1/2都是原方程的解
∴原方程的解是 x1=3/2 ,x2=1/2。
令X/(X-1)=a
a^2-2a-3=0
(a-3)(a+1)=0
a=3或-1
X/X-1=3得X=3/2
X/X-1=-1得X=1/2
x/x-1=y,
y^2-2y=3,
y=3,-1.
x=2/3,1/2
用换元法解x^2/(x-1)^2-2x/x-1=3
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