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Question Number 53769 by ajfour last updated on 25/Jan/19

$$Findmaximumof$$$$\frac{xyz}{(x+a)(x+y)(y+z)(z+b)}.$$

Commented by mr W last updated on 25/Jan/19

$$\frac{1}{16\sqrt{ab}}?$$

Commented by ajfour last updated on 25/Jan/19

$${(a^{1/4}+b^{1/4})}^{-4}Sir.$$

Commented by ajfour last updated on 25/Jan/19

$$longway,Sir.igotitjustnow$$$$\frac{\partial f}{\partial x}=0\Rightarrow x^2=ay$$$$\frac{\partial f}{\partial y}=0\Rightarrow y^2=xz$$$$\frac{\partial f}{\partial z}=0\Rightarrow z^2=by$$$$hencexz=ab$$$$Then{x}^2=a\sqrt{ab},y^2=\sqrt{ab},z^2=b\sqrt{ab}$$$$aftermuchlengthicouldget$$$$f(x,y,z)isthen={(a^{1/4}+b^{1/4})}^{-4}.$$

Commented by mr W last updated on 26/Jan/19

$$youarerightsir!$$$$iconsideredonlythecasea=b.$$

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