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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 \[ \frac x{\sqrt{x^2+1}} +\frac y{\sqrt{y^2+1}} +\frac z{\sqrt{z^2+1}} \]

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  1. KingGeorge
    • 3 years ago
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    It wouldn't just happen to be 1.5 would it?

  2. FoolForMath
    • 3 years ago
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    Yes, what did you used ? ;)

  3. KingGeorge
    • 3 years ago
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    Lucky guess ;)

  4. FoolForMath
    • 3 years ago
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    lol, The options given were tricky so guessing won't work :( The actual solution is very cute and enlightening :)

  5. TuringTest
    • 3 years ago
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    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

  6. ninhi5
    • 3 years ago
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    cross multiply

  7. ninhi5
    • 3 years ago
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    x(y+z) + y(x+z) + z(x+y)

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