Question

if a²+a-²=102,find the value of a-1/a

Answer 1

$102= {a}^{2} + \frac{1}{ {a}^{2} } \\ 102 = ( {a)}^{2} - 2a( \frac{1}{a} ) + {( \frac{1}{a} })^{2} + 2 \\ 102 = ( {a - \frac{1}{a}) }^{2} + 2 \\ 102 = ( {a - \frac{1}{a} })^{2} + 2 \\ ( {a - \frac{1}{a} })^{2} = 102 - 2 = 100 \\ a - \frac{1}{a} = \sqrt{100} \\ a - \frac{1}{a} = 10$
in third step I had add 2 and subtract 2 to make it a perfect square