a+b+c=0 prove that a cube+ b cube +c cube =3abc
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a³+b³ + c³ = 3abc.
Step-by-step explanation:
Now, a³+b³+ c³
= (a+ b + c) (a2 + b2 + c2 – ab – be – ca) + 3abc
[using identity, a³+b³ + c³ – 3 abc = (a + b + c)(a2+b2+c2 –ab–bc-ca)]
= 0 + 3abc [∴ a + b + c = 0]
a³+b³+c³= 3abc.
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