Question

if a+b+c=9 and a^2+b^2+c^2=35, find the value of a^3+b^3+c^3-3abc.​

Answer 1

a+b+c=9 and a2+

+b2+c2=35

Using formula,

(a+b+c)2=a2+b2+c2+2(ab+bc+ca)

92=35+2(ab+bc+ca)

2(ab+bc+ca)=81−35=46

(ab+bc+ca)=23

using formula, 

(a3+b3+c3)−3abc=(a2+b2+c2−ab−bc−ca)(a+b+c)

a3+b3+c3−3abc=(35−23)×9=9×12=108

Answer (B) 108