If $a + b + c = 6$ and $a b + b c + c a = 16$ , find the value of $a^{2} + b^{2} + c^{2}$ .

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Solution

The correct option is A 4
Given $a + b + c = 6$ and $a b + b c + c a = 16$
Using the formula,
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
$6^{2} = a^{2} + b^{2} + c^{2} + 2 (16)$
$36 = a^{2} + b^{2} + c^{2} + 32$
$\Rightarrow a^{2} + b^{2} + c^{2} = 36 - 32 = 4$

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