怎么用凑配法解此题?

问题描述:

怎么用凑配法解此题?
已知f(x+1/x)=x^3+1/x^3+2,求f(x)

令a=x+1/x则a²=x²+2+1/x²x²+1/x²=a²-2所以x³+1/x³=(x+1/x)(x²-1+1/x²)=a(a²-2-1)所以f(a)=a(a²-3)+2=a³-3a+2所以f(x)=x³-3x+2