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If $x > 0, y > 0, x + y = 32$ and $x^{6} + y^{6}$ is minimum then the numbers are

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14, 18

12, 20

16, 16

17, 15

answer is C.

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Detailed Solution

$f (x) = x^{6} + (32 - x)^{6} \Rightarrow f^{1} (x) = 6 x^{5} - 6 (32 - x)^{5} = 0, x = 16 = y$

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