If $a + b + c = 10$ and $a^{2} + b^{2} + c^{2} = 36$ , then $a b + b c + c a =$ ________

136

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64

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32

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none of these

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Solution

The correct option is B $32$
We know, $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$(10)^{2} = 36 + 2 (a b + b c + c a)$
$100 - 36 = 2 (a b + b c + c a)$
$2 (a b + b c + c a) = 64$
$(a b + b c + c a) = 32$

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If $a + b + c = 10$ and $a^{2} + b^{2} + c^{2} = 36$ , then $a b + b c + c a =$ .......... .

\frac{a^{2} + b^{2} + a b}{b^{2} + c^{2} + b c} + \frac{c^{2} + c a + a^{2}}{b^{2} + c^{2} + b c}

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