Question

solve this question pleaseee

Answer 1

we know that,
$( {a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$
similarly ,

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

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

now substitute,
${a}^{2} + \frac{1}{ {a}^{2} } = 11$

${(a - \frac{1}{a} )}^{2} + 2 = 11$

$({a - \frac{1}{a} )}^{2} = 11 - 2 = 9$

$({a - \frac{1}{a} )}^{2} = 9$
by taking square root to both sides.

we get,

$a - \frac{1}{a} = 3$

hope this helps!!!