当x-1/x=3时,(x10+x8+x2+1)/(x10+x6+x4+1)=

题目

当x-1/x=3时,(x10+x8+x2+1)/(x10+x6+x4+1)=

答案

首先你得知道立方和公式：a^3+b^3=(a+b)(a^2-ab+b^2)由x-1/x=3可得(x-1/x)^2=9,即x^2+1/x^2=11,再平方可得x^4+1/x^4=119.所以所求式子=(x^5+x^3+1/x^3+1/x^5)/(x^5+x^4+1/x^4+1/x^5)=(x+1/x)(x^4+1/x^4)/(x^2+1/x^2)...