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National and Regional Contests
Azerbaijan Contests
JBMO TST - Azerbaijan
2017 Azerbaijan JBMO TST
1
Inequality
Inequality
Source: Azerbaijan JBMO TST D1,P1.
May 31, 2017
inequalities
Azerbaijan
Problem Statement
Let
x
,
y
,
z
,
t
x,y,z,t
x
,
y
,
z
,
t
be positive numbers.Prove that
x
y
z
t
(
x
+
y
)
(
z
+
t
)
≤
(
x
+
z
)
2
(
y
+
t
)
2
4
(
x
+
y
+
z
+
t
)
2
.
\frac{xyzt}{(x+y)(z+t)}\leq\frac{(x+z)^2(y+t)^2}{4(x+y+z+t)^2}.
(
x
+
y
)
(
z
+
t
)
x
yz
t
≤
4
(
x
+
y
+
z
+
t
)
2
(
x
+
z
)
2
(
y
+
t
)
2
.
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