解方程3x/(x²-1)+(x²-1)/3x=5/2_数学解答

解方程3x/(x²-1)+(x²-1)/3x=5/2

人气：296 ℃　时间：2020-04-05 05:04:28

解答

令A=3x/(x²-1)原式:A+1/A=5/2 2A^2-5A+2=0(A-2)(2A-1)=0A=2或A=1/2 A=23x=2x^2-22x^2-3x-2=0(x-2)(2x+1)=0x=2或x=-1/2 A=1/2x^2-1=6xx^2-6x-1=0x=3±√10 综上x=2或x=-1/2或x=3±√10