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

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

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

KingGeorge Group TitleBest ResponseYou've already chosen the best response.0
Lucky guess ;)
 2 years ago

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

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
yeah 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
 2 years ago

ninhi5 Group TitleBest ResponseYou've already chosen the best response.0
cross multiply
 2 years ago

ninhi5 Group TitleBest ResponseYou've already chosen the best response.0
x(y+z) + y(x+z) + z(x+y)
 2 years ago
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