x+x负1次方=3,求x的三次方+x的负三次方 的值急应该是18吧

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利用立方和公式a³+b³=(a+b)(a²-ab+b²)=(a+b)[(a+b)²-3ab]即可解答出本题
x³+x^-3
=(x+x^-1)(x^2-1+x^-2)
=(x+x^-1)[(x+x^-1)²-3]
=3×[3²-3]
=3×6=18======以下答案可供参考======
供参考答案1:
x+1/x=3 平方
x^2+2+1/x^2=9
x^2+1/x^2=7
(x+1/x)(x^2+1/x^2)=3*9=27
x^3+1/x+x+1/x^3=27
x^3+3+1/x^3=27
x^3+1/x^3=24