Question

If a+b+c=0 find a^2\bc+b^2\ac+c^2\ab

Answer 1

a^2\bc+b^2\ac+c^2\ab

=(a^3 + b^3 + c^3)/abc -eq 1

a+b+c=0

a+b = -c

cubing both sides

a^3 + b^3 + 3a^2b + 3ab^2 = -c^3

a^3 + b^3 +c^3 = -3ab(a+b)

a^3 + b^3 +c^3 = -3ab(-c)

a^3 + b^3 +c^3 = 3abc

putting value of a^3 + b^3 +c^3 in eq 1

then

a^2\bc+b^2\ac+c^2\ab = (3abc)/abc

a^2\bc+b^2\ac+c^2\ab = 3

answer = 3