- #1
TylerH
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- 0
On this year's Virginia Tech test there was a problem to prove:
[itex]\frac{x}{1+x^2}+\frac{y}{1+y^2}+\frac{z}{1+z^2}\leq \frac{3\sqrt{3}}{2}[/itex]
when
[itex]x+y+z=xyz[/itex]
So my approach was to consider the function, f, where
[itex]f(x, y, z)=\frac{x}{1+x^2}+\frac{y}{1+y^2}+\frac{z}{1+z^2}[/itex]
then restrict f to the plane x+y+z=xyz, then maximize f.
How could I restrict f to that plane and then maximize?
[itex]\frac{x}{1+x^2}+\frac{y}{1+y^2}+\frac{z}{1+z^2}\leq \frac{3\sqrt{3}}{2}[/itex]
when
[itex]x+y+z=xyz[/itex]
So my approach was to consider the function, f, where
[itex]f(x, y, z)=\frac{x}{1+x^2}+\frac{y}{1+y^2}+\frac{z}{1+z^2}[/itex]
then restrict f to the plane x+y+z=xyz, then maximize f.
How could I restrict f to that plane and then maximize?