函数化简求值题若x^(1/2)+x^(-1/2)=3,求【x^(3/2)+x^(-3/2)】/【x^2+x^-2】

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函数化简求值题
若x^(1/2)+x^(-1/2)=3,求【x^(3/2)+x^(-3/2)】/【x^2+x^-2】

x^(1/2)+x^(-1/2)=3
两边平方
x+2+x^(-1)=9
x+x^(-1)=7
两边平方
x^2+2+x^(-2)=49
x^2+x^(-2)=47
x^(3/2)+x^(-3/2)
=[x^(1/2)]^3+[x^(-1/2)]^3
=[x^(1/2)+x^(-1/2)][x-1+x^(-1)]
=3*(7-1)
=18
所以[x^(3/2)+x^(-3/2)]/[x^2+x^(-2)]
=18/47

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