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Iran MO (3rd Round)
1996 Iran MO (3rd Round)
1
Inequality with 4 variables - \sum \frac{a}{b+2c+3d} ≥ 2/3
Inequality with 4 variables - \sum \frac{a}{b+2c+3d} ≥ 2/3
Source: Iran Third Round 1997, E1, P1
March 27, 2011
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be positive real numbers. Prove that
a
b
+
2
c
+
3
d
+
b
c
+
2
d
+
3
a
+
c
d
+
2
a
+
3
b
+
d
a
+
2
b
+
3
c
≥
2
3
.
\frac{a}{b+2c+3d}+\frac{b}{c+2d+3a}+\frac{c}{d+2a+3b}+\frac{d}{a+2b+3c} \geq \frac{2}{3}.
b
+
2
c
+
3
d
a
+
c
+
2
d
+
3
a
b
+
d
+
2
a
+
3
b
c
+
a
+
2
b
+
3
c
d
≥
3
2
.
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