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#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

$4^\sqrt{5x+9y+4z}-68\times2^\sqrt{5x+9y+4z}+256=0$

please find:

$\max(x+y+z)\times \min(x+y+z)$

- Thread starter Albert
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- Thread starter
- #1

- Jan 25, 2013

- 1,225

$4^\sqrt{5x+9y+4z}-68\times2^\sqrt{5x+9y+4z}+256=0$

please find:

$\max(x+y+z)\times \min(x+y+z)$

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- Feb 7, 2012

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- Jan 25, 2013

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from Opalg's mention :

$5x+9y+4z = 4$ or $36$.

for:$4x+4y+4z\leq 5x+4y+9z\leq 9x+9y+9z$

if $5x+4y+9z=4$

then :$4x+4y+4z\leq 4 \leq 9x+9y+9z$

$\therefore x+y+z\geq \dfrac {4}{9}$

if $5x+4y+9z=36$

then :$4x+4y+4z\leq 36 \leq 9x+9y+9z$

$\therefore x+y+z\leq 9$

and we get :$max(x+y+z)\times min(x+y+z)=4$