若x^1/2+x^-1/2=3,求(x^3/2+x^-3/2 -3)/(x^2+x^-2 -2)的值

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若x^1/2+x^-1/2=3,求(x^3/2+x^-3/2 -3)/(x^2+x^-2 -2)的值

若x^1/2+x^-1/2=3,求(x^3/2+x^-3/2 -3)/(x^2+x^-2 -2)的值
若x^1/2+x^-1/2=3,求(x^3/2+x^-3/2 -3)/(x^2+x^-2 -2)的值

若x^1/2+x^-1/2=3,求(x^3/2+x^-3/2 -3)/(x^2+x^-2 -2)的值
x^1/2+x^-1/2=3 两边平方得:x+2+x^-1=9,x+x^-1=7, 两边再平方得:x^2+2+x^-2=49,x^2+x^-2=47 (x^3/2+x^-3/2 -3)/(x^2+x^-2 -2) =[(x^1/2+x^-1/2)(x-1+x^-1)-3 ]/(x^2+x^-2 -2) =[3 ×6-3]/(47-2) =15/45 =1/3