根号x+根号1/x=3,求（x2+1/x2-2）/（x3/2+1/x3/2-3）的值

题目

根号x+根号1/x=3,求（x2+1/x2-2）/（x3/2+1/x3/2-3）的值

答案

根号x+根号1/x=3===>x+1/x=(根号x+根号1/x)^2-2=7x+1/x=7===>x^2+1/x^2=(1/x+x)^2-2=47===>x2+1/x2-2=45x3/2+1/x3/2-3=1/2*(1+1/x)[(1+1/x)^2-3*1*1/x]-3=1/2*7*46-3=158（x2+1/x2-2）/（x3/2+1/x3/2-3）=45/158...