Question

If a+1/a=8 then find the value of a^2+1/a^2

Answer 1

Given :-

$\blue{ \frak{a + \frac{1}{a} =8 }}$

To Find :-

$\green{ \frak{ {a}^{2} + \frac{1}{ {a}^{2} } = \: \: ?}}$

Solution :-

$= > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \rm \bigg(a + \frac{1}{a} \bigg)^{2} = {(8)}^{2} \\ \\ = > \rm {a}^{2} + \frac{1}{ {a}^{2} } + 2( \cancel{a}) \bigg( \frac{1}{ \cancel{a}} \bigg) = 64 \\ \\ \rm= > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 64 \\ \\ = > \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {a}^{2} + \frac{1}{ {a}^{2} } = 64 - 2 \\ \\ = > \boxed{ \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:{a}^{2} + \frac{1}{ {a}^{2}} = \red{62} \: \: \: \: \: \: \: }$