Question

Show that If ∛a + ∛b + ∛c = 0, then: (a + b + c)³ = 27abc

Answer 1

It is an identity as if (a+b+c)=0, then a^3+b^3+c^3=3abc
so,
now it is easy to solve,
cbrt(a)+cbrt(b)+cbrt(c)=0
so,
(cbrt(a))^3+(cbrt(b))^3+(cbrt(c))^3=3(cbrt(abc))
a+b+c=3(cbrt(abc))
Cubing both side,
(a+b+c)^3=27abc...

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