Question

if a≠0 and a-1/a=3 find:
1. a³-1/a³​

Answer 1

Step-by-step explanation:

$a - \frac{1}{a} = 3 \\ {a}^{3 } - \frac{1}{ {a}^{3} } \\ = (a - \frac{1}{a} )( {a}^{2} + a \times \frac{1}{a} + \frac{1}{ {a}^{2} } ) \\ = 3 \times {(a - \frac{1}{a} )}^{2} + 2 \times a \times \frac{1}{a} + a \times \frac{1}{a} \\ = 3( {3}^{2} + 2 + 1) \\ = 3 \times 12 \\ = 36 \: ans.$