用换元法解方程3x/x^-1+x^-1/3x=5/2

题目

用换元法解方程3x/x^-1+x^-1/3x=5/2

答案

设3x/（x^2-1）=t,则t+1/t=5/2,去分母得t^2-5t/2+1=0,即(t-2)(t-1/2)=0,所以t=2或t=1/2,当t=2时得3x/（x^2-1）=2,即2x^2-3x-2=0,解得x=2或x=-1/2,当t=1/2时得3x/（x^2-1）=-1/2,即6x/（x^2-1）=-1即x^2+6x-1=0,解得....