Question

if a+b+c=0,prove that ,a^3+b^3+c^3=3abc​

Answer 1

We know that,

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

Now, put (a+ b+ c) = 0

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

a3 + b3 + c3 – 3abc = 0

a3 + b3 + c3 = 3abc

Hence proved

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