Question

if a+1/a=7 find a^2+1/a^2 and a^4+1/a^4​

Answer 1

$given \\ a + \frac{ 1}{a} = 7 \\ \\ therefore.. \\ {a}^{2} + \frac{1}{ {a}^{2} } = ( {a + \frac{ 1}{a})}^{2} - 2 \times a \times \frac{1}{a} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {7}^{2} - 2 \times 1 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 47$