If $x + y = 3, x y = 5$ , then find the value of $x^{2} + y^{2}$ .

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Solution

Given that

$x + y = 3$

$x y = 5$

$x^{2} + y^{2} + 2 x y = (x + y)^{2}$

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

$\Rightarrow x^{2} + y^{2} = (3)^{2} - 2 (5)$

$\Rightarrow x^{2} + y^{2} = 9 - 10$

$\Rightarrow x^{2} + y^{2} = - 1$

$∴ x^{2} + y^{2} = - 1$ .

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