The sum of square of two numbers is $13$ and there products is $6$ . Then find their sum.

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Solution

Let the numbers be x and y.
$x^{2} + y^{2} = 13$
$x y = 6$

We have
$∴ (x + y)^{2} = x^{2} + y^{2} + 2 x y$
$\Rightarrow (x + y)^{2} = 13 + 2 (6)$
$\Rightarrow (x + y)^{2} = 13 + 12$
$\Rightarrow (x + y)^{2} = 25$
$\Rightarrow x + y = \sqrt{25}$
$\Rightarrow x + y = \pm 5$ .

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