Solution
$$ x^3 + y^3 = 9 $$
x + y = 3
$$ (x + y)^3 = 3^3 $$
$$ x^3 + y^3 + 3xy(x + y) = 27 $$
9 + 3xy(x + y) = 27
3xy(x + y) = 18
xy(x + y) = 6
$$ xy \times 3 = 6 $$
xy = 2
$$ x^2 + y^2 = (x + y)^2 - 2xy $$
$$ x^2 + y^2 = 3^2 - 2 \times 2 $$
$$ x^2 + y^2 = 9 - 4 = 5 $$
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