a\(^2\)+ b\(^2\) + c\(^2\) = 1⇒ \(\left|a\right|\); \(\left|b\right|\) ; \(\left|c\right|\) ≤ 1
⇒ \(\left|a^3\right|\) ≤ a\(^2\) ; \(\left|b^3\right|\) ≤ b\(^2\) ; \(\left|c^3\right|\) ≤ c\(^2\)
⇒a\(^3\)+ b\(^3\)+ c\(^3\) ≤ \(\left|a^3\right|\) + \(\left|b^3\right|\) + \(\left|c^3\right|\) ≤ a\(^2\) + b\(^2\) + c\(^2\) = 1
Dấu "=" xảy ra khi( a;b;c) = (1;0;0) ; (0;1;0) ; (0;0;1)
Vậy S = 0 + 0 + 1 = 1
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