Question

find the value of a^3+b^3+c^3-3abc if a+b+c=5 and a^2 +b^2 +c^2= 29.

Answer 1

a+b+c = 5
squaring both sides,
(a+b+c)^2 = 5^2
a^2+b^2+c^2 + 2(ab+bc+ca)= 25
29+2(ab+bc+ca) = 25
2(ab+bc+ca)= 25-29
ab+bc+ca = -4/2
= -2
a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc -ca)
= 5(29-(-2)
= 5(31)
= 155