Find : $a + b + c$ , if $a^{2} + b^{2} + c^{2} = 83$ and $a b + b c + c a = 71$ .

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Solution

By using formula ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
Substituting $a^{2} + b^{2} + c^{2} = 83; a b + b c + c a = 71$
${(a + b + c)}^{2} = 83 + 2 (71)$
${(a + b + c)}^{2} = 225$
$a + b + c = \sqrt{225} = 15$

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