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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

$\begin{array}{r} x > 0, y > 0 \end{array}$

$\begin{array}{r} x + y = 32 \end{array}$

$\begin{array}{r} if x + y = k, x^{n} + y^{n} is minimum \end{array}$

$\begin{array}{r} \Rightarrow x = y \end{array}$

$\begin{array}{r} x + y = 32 \Rightarrow 2 x = 32 \end{array}$

$\begin{array}{r} \Rightarrow x = 16 \end{array}$

$∴$ numbers are 16,16

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