Question

$a - 1 \div a = 7 find \: a {2 + 1 \div a {2 = }^{2} }^{}$
​

Answer 1

$a - \frac{1}{a} = 7 \\ \\ squaring \: both \: sides \\ \\ (a - \frac{1}{a} ) {}^{2} = 49 \\ {a}^{2} + \frac{1}{ {a}^{2} } - 2 = 49 \\ {a}^{2} + \frac{1}{ {a}^{2} } = 49 + 2 = 51$