已知﹙3x/x²-1﹚﹢﹙x²-1/3x﹚=5/2,解方程求x
1个回答

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