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National and Regional Contests
Romania Contests
Romania Team Selection Test
1993 Romania Team Selection Test
1
Nice!
Nice!
Source:
August 26, 2006
inequalities unsolved
inequalities
Problem Statement
Find max. numbers
A
A
A
wich is true ineq.:
x
y
2
+
z
2
+
y
x
2
+
z
2
+
z
x
2
+
y
2
≥
A
\frac{x}{\sqrt{y^{2}+z^{2}}}+\frac{y}{\sqrt{x^{2}+z^{2}}}+\frac{z}{\sqrt{x^{2}+y^{2}}}\geq A
y
2
+
z
2
x
+
x
2
+
z
2
y
+
x
2
+
y
2
z
≥
A
x
,
y
,
z
x,y,z
x
,
y
,
z
are positve reals numberes! :wink:
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