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If $a + b + c = 8$ and $a b + b c + c a = 18$ , then the value of $(a^{2} + b^{2} + c^{2})$ is

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answer is B.

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Detailed Solution

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

${(8)}^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$

$64 = a^{2} + b^{2} + c^{2} + 2 (18)$

$64 - 36 = a^{2} + b^{2} + c^{2}$

$28 = a^{2} + b^{2} + c^{2}$

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