Question

HELP! :
$a + \frac{1}{a} = \frac{5}{2}$
$a { }^{2} + \frac{1}{a { }^{2} } = ?$

Answer 1

$a+\frac1a=\frac52|^2 \\ \\ (a+\frac1a)^2=\frac{25}{4} \\ \\ a^2+\frac{1}{a^2}+a*2*\frac{1}{a}=\frac{25}{4} \\ \\ a^2+\frac{1}{a^2}+2=\frac{25}{4} \\ \\ a^2+\frac{1}{a^2}=\frac{25}{4}-\frac{8}{4} \\ \\ a^2+\frac{1}{a^2}=\frac{17}{4}$