配凑法解f(x+1/x)=x^3+1/(x^3),求f(x)请详细点

Question

配凑法解f(x+1/x)=x^3+1/(x^3),求f(x)请详细点

Answer 1

f(x+1/x)=x^3+2x^2*1/x+2x*1/x^2+1/x^3-2(x+1/x)
=(x+1/x)^3-2(x+1/x)
f(x)=x^3-2x