已知﹙3x/x²-1﹚﹢﹙x²-1/3x﹚=5/2,解方程求x
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已知﹙3x/x²-1﹚﹢﹙x²-1/3x﹚=5/2,解方程求x
已知﹙3x/x²-1﹚﹢﹙x²-1/3x﹚=5/2,解方程求x
已知﹙3x/x²-1﹚﹢﹙x²-1/3x﹚=5/2,解方程求x
设y=3x/(x²-1),则
y+1/y=5/2
2y²-5y+2=0
(2y-1)(y-2)=0
y=2或y=1/2
于是
(1)3x/(x²-1)=2
3x=2x²-2
2x²-3x-2=0
(2x+1)(x-2)=0
x=2或x=-1/2
(2)3x/(x²-1)=1/2
x²-1=6x
x²-6x=1
(x-3)²=10
x-3=±√10
x=3±√10
所以方程的解为x=2或x=-1/2或x=3±√10