Answer:
5
Step-by-step explanation:
We know that
[tex]x + y = 3[/tex]
and
[tex]xy = 2[/tex]
Solve for x in first variable
[tex]x = 3 - y[/tex]
Substitute this into second equation
[tex](3 - y)y = 2[/tex]
[tex] - {y}^{2} + 3y - 2[/tex]
Simplify
[tex] {y}^{2} - 3y + 2[/tex]
[tex](y - 1)(y - 2)[/tex]
[tex]y = 1[/tex]
[tex]y = 2[/tex]
So x or y can be
[tex]x = 1 \: \: y = 2[/tex]
or
[tex]x = 2 \: \: \: y = 1[/tex]
So we need to find x^2 and y^2.
[tex] {2}^{2} + {1}^{2} = 5[/tex]
