Question

if a square +1/a square =27 than the value of a square a-1/a is​

Answer 1

Given -

${a}^{2} + \frac{1}{ {a}^{2} } = 27$

To find -

$the \: value \: of \: a - \frac{1}{a}$

Solution -

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

By Squaring,

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

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

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

$\implies {(a - \frac{1}{a} )}^{2} = 27 - 2$

$\implies {(a - \frac{1}{a} )}^{2} = 25$

$\implies {(a - \frac{1}{a} )} = \frac{ + }{ - } 25$

$\implies {(a - \frac{1}{a} )} = \frac{ + }{ - } 5$