If a+b+c=0 then prove that a 3 +b 3 +c 3 =3abc
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given ,
a+b+c=0
we need prove that,
a^3+b^3+c^3=3abc {a^3 denotes that a cube where ^ symbol denotes from cube square etc}
proof,
a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2 -ab-bc-ca){as we know
that a+b+c=0 we get}
a^3+b^3+c^3-3abc=(0)(a^2+b^2+c^2-ab-bc-ca)
a^3+b^3+c^3-3abc=0
a^3+b^3+c^3=3abc
hence proved
a+b+c=0
we need prove that,
a^3+b^3+c^3=3abc {a^3 denotes that a cube where ^ symbol denotes from cube square etc}
proof,
a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2 -ab-bc-ca){as we know
that a+b+c=0 we get}
a^3+b^3+c^3-3abc=(0)(a^2+b^2+c^2-ab-bc-ca)
a^3+b^3+c^3-3abc=0
a^3+b^3+c^3=3abc
hence proved
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