Question

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

Answer 1

We have,
$${\left(x+y\right)}^2=x^2+y^2+2xy$$
$$\Rightarrow {12}^2=x^2+y^2+2\times 32$$
$$\Rightarrow 144=x^2+y^2+64$$
$$\Rightarrow 144-64=x^2+y^2$$
$$\Rightarrow x^2+y^2=80$$