If $a + b + c = 9$ and $2 (a b + b c + c a) = 52$ ,
then $a^{2} + b^{2} + c^{2}$ is _____.

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Solution

The correct option is A 29
Given, $a + b + c = 9$ and $2 (a b + b c + c a) = 52$ .

Using the identity, $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a = a^{2} + b^{2} + c^{2} + 2 (a b + b c + a c)$ ,
$\Rightarrow$ $9^{2} = a^{2} + b^{2} + c^{2} + 52$
$\Rightarrow$ $a^{2} + b^{2} + c^{2} = 9^{2} - 52$
= $81 - 52$
= $29$ .

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