Question

if a-1/a=p then a³+1/a³=?​

Answer 1

Answer:

your solution is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: find : \\ a {}^{3} + \frac{1}{a {}^{3} } \\ \\ given \: that : \\ a - \frac{1}{a} = p \\ \\ we \: \: know \: that \\ (a - \frac{1}{a} \: ) {}^{3} = a {}^{3} + \frac{1}{ {a {}^{3} } } - 3a {}^{2} \times \frac{1}{a} + 3a \times \frac{1}{a {}^{2} } \\ \\ p {}^{3} = a {}^{3} + \frac{1}{a {}^{3} } - 3a + \frac{3}{a} \\ \\ a {}^{3} + \frac{1}{a {}^{3} } = p {}^{3} + 3a - \frac{3}{a} \\ \\ = p {}^{3} + 3(a - \frac{1}{a} \: ) \\ \\ = p {}^{3} + 3p$