If ³√a + ³√b = ³√c , then

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Given , ³√a + ³√b = ³√c
⇒ ³√a + ³√b - ³√c = 0
∴ a + b – c = -3(abc)^{1 / 3}
On cubing both sides,
(a + b – c)³ = -27abc
∴ (a + b – c)³ + 27abc = 0