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If a + b + c = 14 and a 2 + b 2 + c 2 = 96, then (ab + bc + ca) =?

Correct Answer: 50

Explanation:

We know that,
(a + b + c)2 = (a2 + b2 + c2) + 2(ab + bc + ca )
⇒ 196 = 96 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 196 - 96 = 100
∴ (ab + bc + ca) = 100/2 = 50


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