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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68

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Solution

The correct option is C $32$
$a + b + c = 10$
Squaring on both sides, we get
$a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a = 100$
$36 + 2 (a b + b c + c a) = 100$
$2 (a b + b c + c a) = 100 - 36 = 64$
$a b + b c + c a = \frac{64}{2} = 32$

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Similar questions

a + b + c = 10

a^{2} + b^{2} + c^{2} = 36

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}

If (a+b+c) = 12 and a $^{2}$ +b $^{2}$ +c $^{2}$ = 108, then (ab+bc+ca) = ?

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