已知f(x+1/x)=x^2+1/x^2+1/x则f(x)

Question

已知f(x+1/x)=x^2+1/x^2+1/x则f(x)

Answer 1

令x+1/x=t,解得x=[t±√（t²-4）]/2 1/x=2/[t±√（t²-4）]
t²=x²+1/x²+2 x²+1/x²=t²-2
f(t)=t²-2+2/[t±√（t²-4）]