If $a + b + c = 10,$ $a^{2} + b^{2} + c^{2} = 60,$ find the value of $a b + b c + c a$ .

10

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20

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25

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30

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Solution

The correct option is A $20$
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
$10^{2} = 60 + 2 (a b + b c + c a)$
$a b + b c + c a = \frac{100 - 60}{2} = 20$

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Similar questions

a + b + c = 10

a b + b c + c a = 25

a^{2} + b^{2} + c^{2} .

a^{2} + b^{2} + c^{2} = 20

a + b + c = 0

a b + b c + c a + 10

If $a^{2} + b^{2} + c^{2} = 16$ and ab + bc + ca = 10, find the value of a + b + c.

a^{2} + b^{2} + c^{2} = 60

a b + b c + c a = 42

a + b + c

\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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