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2006 Moldova Team Selection Test
3
Moldova tst iii, problem 3
Moldova tst iii, problem 3
Source: Moldova TST III
March 26, 2006
inequalities
inequalities proposed
Problem Statement
Positive real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
satisfy the relation
a
b
c
=
1
abc=1
ab
c
=
1
. Prove the inequality:
a
+
3
(
a
+
1
)
2
+
b
+
3
(
b
+
1
)
2
+
c
+
3
(
c
+
1
)
2
≥
3
\frac{a+3}{(a+1)^{2}}+\frac{b+3}{(b+1)^{2}}+\frac{c+3}{(c+1)^{2}}\geq3
(
a
+
1
)
2
a
+
3
+
(
b
+
1
)
2
b
+
3
+
(
c
+
1
)
2
c
+
3
≥
3
.
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