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2013 VTRMC
Problem 5
Problem 5
Part of
2013 VTRMC
Problems
(1)
2013 VTRMC #5
Source: 35th Annual Virginia Tech Regional Mathematics Contest 2013
9/1/2018
Prove that
x
1
+
x
2
+
y
1
+
y
2
+
z
1
+
z
2
≤
3
3
2
\frac{x}{\sqrt{1+x^2}}+\frac{y}{\sqrt{1+y^2}}+\frac{z}{\sqrt{1+z^2}} \leq\frac{3\sqrt{3}}{2}
1
+
x
2
x
+
1
+
y
2
y
+
1
+
z
2
z
≤
2
3
3
for any positive real numbers
x
,
y
,
z
x, y,z
x
,
y
,
z
such that
x
+
y
+
z
=
x
y
z
.
x+y+z = xyz.
x
+
y
+
z
=
x
yz
.
[url=https://artofproblemsolving.com/community/c7h236610p10925499]2008 VTRMC #1 [url=http://www.math.vt.edu/people/plinnell/Vtregional/solutions.pdf]here
inequalities