解方程3x/(x²-1)+(x²-1)/3x=5/2
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![解方程3x/(x²-1)+(x²-1)/3x=5/2](/uploads/image/z/581456-56-6.jpg?t=%E8%A7%A3%E6%96%B9%E7%A8%8B3x%2F%28x%26%23178%3B-1%29%2B%28x%26%23178%3B-1%29%2F3x%3D5%2F2)
解方程3x/(x²-1)+(x²-1)/3x=5/2
解方程3x/(x²-1)+(x²-1)/3x=5/2
解方程3x/(x²-1)+(x²-1)/3x=5/2
令A=3x/(x²-1)
原式:A+1/A=5/2
2A^2-5A+2=0
(A-2)(2A-1)=0
A=2或A=1/2
A=2
3x=2x^2-2
2x^2-3x-2=0
(x-2)(2x+1)=0
x=2或x=-1/2
A=1/2
x^2-1=6x
x^2-6x-1=0
x=3±√10
综上x=2或x=-1/2或x=3±√10