已知f(x+1/x)=x平方+1/x平方+1/x,求fx

Question

已知f(x+1/x)=x平方+1/x平方+1/x,求fx

Answer 1

令x+1/x=t,则X=1/(t-1),带入原式可得,f(t)=(t-1)^2+1/(t-1)^2+1/(t-1),令t=x,则f(x)=(x-1)^2+1/(x-1)^2+1/(x-1).