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Contests
National and Regional Contests
Greece Contests
Greece National Olympiad
2000 Greece National Olympiad
3
3
Part of
2000 Greece National Olympiad
Problems
(1)
Best constant
Source: Greek national M.O. 2000, Final Round, problem 3
11/20/2011
Find the maximum value of
k
k
k
such that
x
y
(
x
2
+
y
2
)
(
3
x
2
+
y
2
)
≤
1
k
\frac{xy}{\sqrt{(x^2 + y^2)(3x^2 + y^2)}}\leq \frac{1}{k}
(
x
2
+
y
2
)
(
3
x
2
+
y
2
)
x
y
≤
k
1
holds for all positive numbers
x
x
x
and
y
.
y.
y
.
inequalities unsolved
inequalities