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FoolForMath
 3 years ago
Just another super easy problem,
Let \(x, y, z \in \mathbb{R}^+\) such that \(x +y +z =\sqrt{3} \) . Find the maximum value of \[ \frac x{\sqrt{x^2+1}} +\frac y{\sqrt{y^2+1}} +\frac z{\sqrt{z^2+1}} \]
FoolForMath
 3 years ago
Just another super easy problem, Let \(x, y, z \in \mathbb{R}^+\) such that \(x +y +z =\sqrt{3} \) . Find the maximum value of \[ \frac x{\sqrt{x^2+1}} +\frac y{\sqrt{y^2+1}} +\frac z{\sqrt{z^2+1}} \]

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KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0It wouldn't just happen to be 1.5 would it?

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.0Yes, what did you used ? ;)

FoolForMath
 3 years ago
Best ResponseYou've already chosen the best response.0lol, The options given were tricky so guessing won't work :( The actual solution is very cute and enlightening :)

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.0yeah I see it as there being two options, the boundaries of \(x+y+z=\sqrt3\) or the average where \(x=y=z=\frac{\sqrt3}3\) what kind of proof you want that this is the maximum I'm not sure; you could use calculus I would imagine

ninhi5
 3 years ago
Best ResponseYou've already chosen the best response.0x(y+z) + y(x+z) + z(x+y)
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