- #1
Saitama
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Homework Statement
Find the largest possible value of
[tex]\sqrt{(x-20)(y-x)}+\sqrt{(140-y)(20-x)}+\sqrt{(x-y)(y-140)}[/tex]
subject to ##-40≤x≤100## and ##-20≤y≤200##.
Homework Equations
The Attempt at a Solution
Factoring out ##\sqrt{(x-20)(y-x)(140-y)}## the given expression can be written as
[tex]\sqrt{(x-20)(y-x)(140-y)}\left(\frac{1}{\sqrt{140-y}}+\frac{1}{\sqrt{x-y}}+\frac{1}{\sqrt{x-20}}\right)[/tex]
From the above equation, ##x≠y##, ##x>20##, ##x>y## and ##y<140##.
Hence, ##20≤x≤100## and ##-20≤y≤100##.
But now I am stuck here. I have no clue about how should I proceed further. :(
Any help is appreciated. Thanks!