If $(a + b + c)$ is positive and $a^{2} + b^{2} + c^{2} = 83$ and $a b + b c + c a = 71$

then $a + b + c =$ ___

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Solution

$(a + b + c)^{2} = (a^{2} + b^{2} + c^{2}) + 2 (a b + b c + c a)$

$(a + b + c)^{2} = 83 + 2 (71) = 83 + 142 = 225$

$(a + b + c) = \sqrt{225} = \pm 15$

$∵ (a + b + c) i s p o s i t i v e, a + b + c = 15$

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