If $(a^{2} + b^{2} + c^{2}) = 50$ and $(a c + b c + c a) = 47$ , find the value of $(a + b + c)$

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Solution

$(a^{2} + b^{2} + c^{2}) = 50; (a b + b c + c a) = 47$
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
$(a + b + c)^{2} = 50 + 2 (47)$
$(a + b + c)^{2} = 50 + 94$
$(a + b + c)^{2} = 144$
$(a + b + c) = \sqrt{144} = 12$
$∴ (a + b + c) = 12$

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