Question

If $x+y=12$ and $xy=32$, find the value of $x^2+y^2$.

Answer 1

$x+y=12$

$\Rightarrow {(x+y)}^2={12}^2=144$

$\Rightarrow x^2+y^2+2xy=144$

$\Rightarrow x^2+y^2=144-2xy$

$\Rightarrow x^2+y^2=144-2\times 32$ since $xy=32$

$\Rightarrow x^2+y^2=144-64=80$

$\therefore x^2+y^2=80$