Question

if a-1/a=5,then a^2+1/a^2=?

Answer 1

a -1/a = 5

squaring both sides

(a -1/a)² = 5²

a² -2 + 1/a² = 25

a² + 1/a² = 27

Answer 2

$Answer \: \\ \\ GIVEN \: \: \: QUESTION \: \: Is \: \: \: \\ \\ a - \frac{1}{ a} = 5 \: \: \: \: \: find \: \: \: a {}^{2} + \frac{1}{a {}^{2} } \\ \\ a - \frac{1}{a} = 5 \\ Squaring \: \: \: on \: both \: sides \: we \: have \: \\ \\ (a - \frac{1}{a}) {}^{2} = 5 {}^{2} \\ \\ a {}^{2} + \frac{1}{a {}^{2} } - 2 \times \frac{a}{a} = 25 \\ \\ a {}^{2} + \frac{1}{a {}^{2} } = 25 + 2 \\ \\ a {}^{2} + \frac{1}{a {}^{2} } = 27 \\ \\ Note \: \: \: \\ \\ (a - b) {}^{2} = a {}^{2} + b {}^{2} - 2ab$