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Balkan MO
2012 Balkan MO
2
2
Part of
2012 Balkan MO
Problems
(1)
Inequality involving x, y and z
Source: Balkan MO 2012 - Problem 2
4/28/2012
Prove that
∑
c
y
c
(
x
+
y
)
(
z
+
x
)
(
z
+
y
)
≥
4
(
x
y
+
y
z
+
z
x
)
,
\sum_{cyc}(x+y)\sqrt{(z+x)(z+y)} \geq 4(xy+yz+zx),
cyc
∑
(
x
+
y
)
(
z
+
x
)
(
z
+
y
)
≥
4
(
x
y
+
yz
+
z
x
)
,
for all positive real numbers
x
,
y
x,y
x
,
y
and
z
z
z
.
function
trigonometry
triangle inequality
rearrangement inequality
Balkan