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

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KingGeorgeBest ResponseYou've already chosen the best response.0
It wouldn't just happen to be 1.5 would it?
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.0
Yes, what did you used ? ;)
 one year ago

FoolForMathBest 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 :)
 one year ago

TuringTestBest 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
 one year ago

ninhi5Best ResponseYou've already chosen the best response.0
x(y+z) + y(x+z) + z(x+y)
 one year ago
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