If a²+ b² + c² = 83 and a + b + c = 15, then

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If a²+ b² + c² = 83 and a + b + c = 15, then the value of (ab + bc + ca) is :

1. 69
2. 70
3. 71
4. 72

Correct Option: C

a² + b² + c² = 83
a + b + c = 15
∴ (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
⇒ (15)² = 83 + 2 (ab + bc + ca)
⇒ 225 – 83 = 2(ab + bc + ca)
⇒ 142 = 2 (ab + bc + ca)
⇒ ab + bc + ca = 142/2
= 71