Question

If a+1/a =p, prove that a*3+ 1/a*3=p(p*2-3)

Answer 1

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${a}^{3} + \frac{1}{ {a}^{3} } = (a + \frac{1}{a} ) ^{3} - 3(a + \frac{1}{a} ) \\ = {p}^{3} - 3p \\ = p( {p}^{2} - 3)$