Question

a+b+c=0, a²(b+c)+b²(c+a)+c²(a+b)+3abc=0

Answer 1

Step-by-step explanation:

Since ,

a + b+ c = 0

→ a^3 + b^3 + c^3 = 3abc

Also ,

a+b = -c

b+c = -a

c+a= -b

Now , a^2(b+c)+b^2(c+a)+c^2(a+b) + 3abc

= a^2(-a)+ b^2(-b)+c^2(-c) + 3abc

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

= -(3abc)+3abc

=0