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根号x+根号1/x=3,求（x2+1/x2-2）/（x3/2+1/x3/2-3）的值
题目详情
根号x+根号1/x=3,求（x2+1/x2-2）/（x3/2+1/x3/2-3）的值
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答案和解析
根号x+根号1/x=3===>x+1/x=(根号x+根号1/x)^2-2=7
x+1/x=7===>x^2+1/x^2=(1/x+x)^2-2=47===>x2+1/x2-2=45
x3/2+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
x+1/x=7===>x^2+1/x^2=(1/x+x)^2-2=47===>x2+1/x2-2=45
x3/2+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
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