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Junior Balkan MO
2004 Junior Balkan MO
1
1
Part of
2004 Junior Balkan MO
Problems
(1)
Not too difficult
Source: JbMO 2004, PROBLEM 1
7/20/2004
Prove that the inequality
x
+
y
x
2
−
x
y
+
y
2
≤
2
2
x
2
+
y
2
\frac{ x+y}{x^2-xy+y^2 } \leq \frac{ 2\sqrt 2 }{\sqrt{ x^2 +y^2 } }
x
2
−
x
y
+
y
2
x
+
y
≤
x
2
+
y
2
2
2
holds for all real numbers
x
x
x
and
y
y
y
, not both equal to 0.
inequalities
analytic geometry
calculus
inequalities proposed
algebra