根号x+根号1/x=3,求(x2+1/x2-2)/(x3/2+1/x3/2-3)的值
问题描述:
根号x+根号1/x=3,求(x2+1/x2-2)/(x3/2+1/x3/2-3)的值
答
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...