[高一数学]已知x^1/2-x^(-1/2)=3,求【x^3/2+x^(-3/2)】/[x^1/2+x^(-1/2)]的值.

题目

[高一数学]已知x^1/2-x^(-1/2)=3,求【x^3/2+x^(-3/2)】/[x^1/2+x^(-1/2)]的值.
因为 x^3/2+x^(-3/2) = [x^1/2+x^(-1/2)] [x - x^1/2 * x^(-1/2) + x^(-1) ]
所以 [x^3/2+x^(-3/2)]/[x^1/2+x^(-1/2)] = x - x^1/2 * x^(-1/2) + x^(-1) = x + (1/x) -1
因为 x + (1/x) = [x^1/2-x^(-1/2)]^2 +2 = 11
所以 [x^3/2+x^(-3/2)]/[x^1/2+x^(-1/2)] = 11-1 = 10 .
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中x^3/2+x^(-3/2) = [x^1/2+x^(-1/2)] [x - x^1/2 * x^(-1/2) + x^(-1) ]是什么公式就行.

答案

“立方和”公式a^3+b^3=(a+b)(a^2-ab+b^2)：把x^1/2当成a,则x^3/2＝a^3；把x^(-1/2)当成b,则x^(-3/2)＝b^3. 因为 x^3/2+x^(-3/2) = [x^1/2+x^(-1/2)] [x - x^1/2 * x^(-1/2) + x^(-1) ]所以 [x^3/2+x^(-3/2)]/[x^1/2...