If a + b + c = 15 and a2 + b2 + c2 = 83 then the value of

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If a + b + c = 15 and a² + b² + c² = 83 then the value of a³ + b³ + c³ – 3abc

1. 200
2. 180
3. 190
4. 210

Correct Option: B

a + b + c = 15
∴ (a + b + c)² = 225
∴ a² + b² + c² + 2 (ab + bc + ca)
= 225
⇒ 2 (ab + bc + ca) = 225 – 83
= 142
⇒ ab + bc + ca = 142 ÷ 2 = 71
∴ a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)
= 15 (83 – 71) = 15 × 12 = 180