Complex Numbers

${x}^{3}+{y}^{3}=(x+y)({x}^{2}-xy+{y}^{2})$. 

$5=2({x}^{2}-xy+{y}^{2})$

${x}^{2}-xy+{y}^{2}=\frac{5}{2}$

Because ${x}^{2}-xy+{y}^{2}={(x+y)}^{2}-3xy$

${(x+y)}^{2}-3xy=\frac{5}{2}$.

${2}^{2}-3xy=\frac{5}{2}$

$-3xy=-\frac{3}{2}$

$xy=\frac{1}{2}$

${x}^{2}+{y}^{2}={(x+y)}^{2}-2xy=4-1=3$.

So x²+y² is 3.