Question

If p-1/p=8,find the value p^3-1/p^3​

Answer 1

$you \: know \: \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = {k}^{3} - 3k \\ \\ \\ \\ so \\ \\ \\ p - \frac{1}{p} = 8 \\ \\ k = 8 \\ \\ \\ \\ {p}^{3} - \frac{1}{ {p}^{3} } = {8}^{3} - (3 \times 8) = \\ = {8}^{3} - 24 \\ \\ \\ = 512 - 24 = 488$

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