## 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 $\frac x{\sqrt{x^2+1}} +\frac y{\sqrt{y^2+1}} +\frac z{\sqrt{z^2+1}}$

1. KingGeorge

It wouldn't just happen to be 1.5 would it?

2. FoolForMath

Yes, what did you used ? ;)

3. KingGeorge

Lucky guess ;)

4. FoolForMath

lol, The options given were tricky so guessing won't work :( The actual solution is very cute and enlightening :)

5. TuringTest

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

cross multiply

7. ninhi5

x(y+z) + y(x+z) + z(x+y)