换元法解方程((x^2)/(X-1))^2-((3x^2)/(x-1))-4=0需步骤
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换元法解方程((x^2)/(X-1))^2-((3x^2)/(x-1))-4=0需步骤
换元法解方程((x^2)/(X-1))^2-((3x^2)/(x-1))-4=0需步骤
换元法解方程((x^2)/(X-1))^2-((3x^2)/(x-1))-4=0需步骤
令(x^2)/(X-1)=t
原式化为 t^2-3t-4=0
t=-1, t=4
即(x^2)/(X-1)=-1或4
(1)(x^2)/(X-1)=-1
即x^2+x-1=0
x=(-1+根号5)/2 或 x=(-1-根号5)/2
(2)(x^2)/(X-1)=4
即x^2-4x+4=0
(x-2)^2=0
所以x=2
综合(1)(2)x=(-1+根号5)/2 或 x=(-1-根号5)/2或x=2
令(x^2)/(X-1)=t
原式化为 t^2-3t-4=0
t=-1, t=4
即(x^2)/(X-1)=1或4
(1)(x^2)/(X-1)=1
即x^2-x+1=0
因为判别式小于0,此方程无解
(2)(x^2)/(X-1)=4
即x^2-4x+4=0
(x-2)^2=0
所以x=2