类似此题要怎么用换元法f(x+1/x)=x^2+1/x^2求f(x)只能用分离法么?

Question

类似此题要怎么用换元法
f(x+1/x)=x^2+1/x^2 求f(x) 只能用分离法么?

Answer 1

f(x+1/x)=x^2+1/x^2=（x+1/x）²-2
令x+1/x=t,则f(t)=t²-2
所以f(x)=x²-2