Correct Answer: 180

Solution : Given: a ² +b ² +c ² = 83, a+b+c = 15
We know that,
(a + b + c) ² = a ² + b ² + c ² + 2(ab + bc + ca)
⇒ (15) ² = 83 + 2(ab + bc + ca)
⇒ 225 – 83 = 2(ab + bc + ca)
⇒$\frac{142}{2}$ = ab + bc + ca
$\therefore$ ab + bc + ca = 71
Now, a ³ + b ³ + c ³ –3abc = (a + b + c)(a ² + b ² + c ² – ab – bc – ca)
Putting the values, we get:
= (15)(83 – 71)
= 15 × 12
= 180
Hence, the correct answer is 180.