Evaluate If a + b + c = 15 and $a^{2} + b^{2} + c^{2}$ = 125 , find ab + bc + ca

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100

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Solution

The correct option is B
50

We use the identity $(a + b + c)^{2}$ = $a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

Given a + b + c = 15 and $a^{2} + b^{2} + c^{2}$ = 125

Hence $(15)^{2}$ = $125 + 2 (a b + b c + c a)$

$225 = 125 + 2 (a b + b c + c a)$

$225 - 125 = 2 (a b + b c + c a)$

$100 = 2 (a b + b c + c a)$

Hence $a b + b c + c a$ = 50

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