Find-maximum-of-xyz-x-a-x-y-y-z-z-b-

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

F i n d m a x i m u m o f

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

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

\frac{1}{16 \sqrt{a b}} ?

Commented by ajfour last updated on 25/Jan/19

{(a^{1 / 4} + b^{1 / 4})}^{- 4} S i r .

Commented by ajfour last updated on 25/Jan/19

l o n g w a y, S i r . i g o t i t j u s t n o w

\frac{\partial f}{\partial x} = 0 \Rightarrow x^{2} = a y

\frac{\partial f}{\partial y} = 0 \Rightarrow y^{2} = x z

\frac{\partial f}{\partial z} = 0 \Rightarrow z^{2} = b y

h e n c e x z = a b

T h e n x^{2} = a \sqrt{a b}, y^{2} = \sqrt{a b}, z^{2} = b \sqrt{a b}

a f t e r m u c h l e n g t h i c o u l d g e t

f (x, y, z) i s t h e n = {(a^{1 / 4} + b^{1 / 4})}^{- 4} .

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

y o u a r e r i g h t s i r!

i c o n s i d e r e d o n l y t h e c a s e a = b .

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