※ 引述《adamchi (adamchi)》之銘言：
: 1.若0<x<1,且x+1/x=3
: 求x^3 - 1/(x^3) = ?
同乘x移項
x^2-3x+1 = 0，求得x = (3±√5)/2 (大於1不合)
x^2 = 3x-1
x^3 = x^2*x = (3x-1)*x = 3x^2-x = 3(3x-1)-x = 9x-3-x = 8x-3 = 8(3-√5)/2-3
= 9-4√5
1/(x^3) = 1/(9-4√5)
= 9+4√5
x^3 - 1/(x^3) = (9-4√5) - (9+4√5)
= -8√5
: 答:-8*5^(1/2)
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