Question

a-1/a=3,the value of a2-1/a²​

Answer 1

Step-by-step explanation:

$a - \frac{1}{a} = 3 \\ \\ On \: squaring \: both \: sides \\ {(a - \frac{1}{a} )}^{2} = {3}^{2} \\ = > {a}^{2} + { \frac{1}{a}}^{2} - 2 = 9 \\ = > {a}^{2} + { \frac{1}{a} }^{2} = 9 + 2 \\ = > {a}^{2} + { \frac{1}{a} }^{2} = 11\\ \\ Now \: adding \: 2 \: both \: sides \\ \\ {a}^{2} + { \frac{1}{a} }^{2} + 2 = 9 + 2 \\ = > {(a + \frac{1}{a} )}^{2} = 13 \\ = > a + \frac{1}{a} = \sqrt{13} \\ \\ Now \\ {a}^{2} - {\frac{1}{a}}^{2} =( a + \frac{1}{a} )(a - \frac{1}{a} ) \\ = > {a}^{2} - {\frac{1}{a}}^{2} = \sqrt{13} \times \: 3 \\ = > {a}^{2} - {\frac{1}{a}}^{2} = 3 \sqrt{13} \\ \\ Hope \: it \: helps \: you...... \\ Please \: mark \: my \: answer \: as \: \\ brainleist......$