若X+1/X＝3则X＾2/X＾4+X＾2+1＝＿＿＿＿
问题描述：
若X+1/X＝3则X＾2/X＾4+X＾2+1＝＿＿＿＿
答
8
X＾2/X＾4+X＾2+1＝1/X＾2+X＾2+1=(X+1/X)^2-1=8
答
x+1/x=3,两边平方,
x^2+1/x^2+2=9
x^2+1/x^2=7
(x^4+x^2+1)/x^2=x^2+1+1/x^2=7+1=8
x^2/(x^4+x^2+1) = 1 / [(x^4+x^2+1)/x^2] = 1/8