Question

If a + b = 5 and ab = 6, find $a^2+b^2$.

Answer 1

$(a+b{)}^2=a^2+b^2+2ab$
$\Rightarrow (5{)}^2=a^2+b^2+2\times 6$
$\Rightarrow 25=a^2+b^2+12$
$\Rightarrow 25-12=a^2+b^2$
$\Rightarrow 13=a^2+b^2$
$\therefore a^2+b^2=13$