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

If a + b + c = 15 and a² + b² + c² = 83, find the value of a³ + b�

1.	If a + b + c = 15 and a² + b² + c² = 83, find the value of a³ + b³ + c³ – 3abc.
Answer» a² + b² + c² = 83 ------(1)a + b+ c = 15On squaring both sides, we geta² + b² + c² + 2( ab + bc + ca) = 225=> 83 + 2 ( ab + bc + ca) = 225=> 2 ( ab + bc + ca) = 142=> ab + bc + ca = 71 --------(2)Now,a³ + b³ + c³- 3abc = ( a +b + c) (a² + b² + c² - ab - bc - ca)= ( 15) [ 83 - (ab + bc + ca)]= (15)(83-71)= 15 × 12= 180\xa0