If a + b + c = 15 and a2 + b2 + c2 = 83, then a3 + b3 +

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If a + b + c = 15 and a² + b² + c² = 83, then a³ + b³ + c³ – 3abc = ?

1. 160
2. 175
3. 180
4. 100

Correct Option: C

a³ + b³ + c³ – 3abc = (a + b + c)
(a² + b² + c² – ab – bc – ca)
Now, (a + b + c)² = a² + b² + c² + 2 (ab + bc + ca)
⇒ 15² = 83 + 2 (ab + bc + ca)
⇒ 225 = 83 + 2 (ab + bc + ca)
⇒ 142 = 2 (ab + bc + ca)

⇒ ab + bc + ca =	142	= 71
	2

∴ a³ + b³ + c³ – 3abc = 15 × (83 – 71) = 15 × 12 = 180