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if a+b+c=0 then, a cube + b cube + c cube

it is given that a + b + c = 0

we know that-

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

a3 + b3 + c3 - 3abc = (0)(a2 + b2 + c2 - ab - bc - ac)

a3 + b3 + c3 - 3abc = 0

a3 + b3 + c3 = 3abc

  • 39
View Full Answer

a+b+c=0

=a+b=-c

Cubing both sides

(a+b)3=-c3

a3+b3+3ab(a+b)=-c3

Since a+b=-c

Therefore

a3+b3+3ab(-c)=-c

a3+b3-3abc=-c

a3+b3+c3=3abc

  • 6
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