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Mediterranean Mathematics Olympiad
2013 Mediterranean Mathematics Olympiad
3
3
Part of
2013 Mediterranean Mathematics Olympiad
Problems
(1)
\sum (xy)^{2}=6xyz
Source: MMC 2013
6/14/2013
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be positive reals for which:
∑
(
x
y
)
2
=
6
x
y
z
\sum (xy)^{2}=6xyz
∑
(
x
y
)
2
=
6
x
yz
Prove that:
∑
x
x
+
y
z
≥
3
\sum \sqrt{\frac{x}{x+yz}}\geq \sqrt{3}
∑
x
+
yz
x
≥
3
.
inequalities
inequalities proposed