Question

If a+b+c=0 prove that a 3 +b 3 +c 3 =3abc

Answer 1

we know that [tex] a^{3}+ b^{3} + c^{3}=(a+b+c)( a^{2} +b^{2}+c^{2} -ab-bc-ca)+3abc
substitue (a+b+c)=0 in above equation

a^{3}+ b^{3} + c^{3}=0*(a^{2} +b^{2}+c^{2} -ab-bc-ca)+3abc
a^{3}+ b^{3} + c^{3}=3abc