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2012 CIIM
Problem 3
CIIM 2012 Problem 3
CIIM 2012 Problem 3
Source:
June 9, 2016
CIIM
CIIM 2012
undergraduate
Problem Statement
Let
a
,
b
,
c
,
a,b,c,
a
,
b
,
c
,
the lengths of the sides of a triangle. Prove that
(
3
a
+
b
)
(
3
b
+
a
)
(
2
a
+
c
)
(
2
b
+
c
)
+
(
3
b
+
c
)
(
3
c
+
b
)
(
2
b
+
a
)
(
2
c
+
a
)
+
(
3
c
+
a
)
(
3
a
+
c
)
(
2
c
+
b
)
(
2
a
+
b
)
≥
4.
\sqrt{\frac{(3a+b)(3b+a)}{(2a+c)(2b+c)}} + \sqrt{\frac{(3b+c)(3c+b)}{(2b+a)(2c+a)}} + \sqrt{\frac{(3c+a)(3a+c)}{(2c+b)(2a+b)}} \geq 4.
(
2
a
+
c
)
(
2
b
+
c
)
(
3
a
+
b
)
(
3
b
+
a
)
+
(
2
b
+
a
)
(
2
c
+
a
)
(
3
b
+
c
)
(
3
c
+
b
)
+
(
2
c
+
b
)
(
2
a
+
b
)
(
3
c
+
a
)
(
3
a
+
c
)
≥
4.
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