已知函数x+x^-1=3则x^(3/2)+x^(-3/2)的值为

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已知函数x+x^-1=3则x^(3/2)+x^(-3/2)的值为已知函数x+x^-1=3则x^(3/2)+x^(-3/2)的值为已知函数x+x^-1=3则x^(3/2)+x^(-3/2)的值为令a=x

已知函数x+x^-1=3则x^(3/2)+x^(-3/2)的值为
已知函数x+x^-1=3则x^(3/2)+x^(-3/2)的值为

已知函数x+x^-1=3则x^(3/2)+x^(-3/2)的值为
令 a = x^(1/2) ,b = x^(-1/2) ,则:ab = 1
已知,x^+x^(-1)=3,即a^2+b^2 = 3
(a+b)^2=a^2+b^2+2ab=3+2=5
a +b=±√5
x^(3/2)+x^(-3/2)
=a^3+b^3
=(a+b)(a^2+b^2-ab)
=±√5*(3-1)
=±2√5