# If $x + y = 12$and$xy = 32$, find the value of ${x^2} + {y^2}$.
${\left( {x + y} \right)^2} = {x^2} + {y^2} + 2xy$
$\Rightarrow \,\,{12^{2\,}} = {x^2} + {y^2} + 2 \times 32$
$\Rightarrow \,\,144 = {x^2} + {y^2} + 64$
$\Rightarrow 144 - 64 = {x^2} + {y^2}$
$\Rightarrow {x^2} + {y^2} = 80$