If a + b + c is equal to 12 and $a^{2} + b^{2} + c^{2} = 50$ . Then, find the value of ab + bc + ca

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Solution

a + b + c = 12
$a^{2} + b^{2} + c^{2} = 50$
$∴$ ab + bc + ca = ?
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$ (Standard Identity)
$12^{2} =$ 50+ 2 (ab + bc + ca)
$\Rightarrow$ 144 - 50 = 2 (ab + bc + ca)
$\Rightarrow$ 94 = 2(ab + bc + ca)
$\Rightarrow a b + b c + c a = \frac{94}{2} = 47$

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a + b + c = 12

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