If a + b + c = 14 and a2 + b2 + c2 = 96, then (ab + bc

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If a + b + c = 14 and a² + b² + c² = 96, then (ab + bc + ca) = ?

1. 51
2. 55
3. 50
4. 65
5. None of the above

Correct Option: C

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