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Iran Contests
Iran Team Selection Test
2008 Iran Team Selection Test
5
sqrt{a^3 + a} + sqrt{b^3+b} + sqrt{c^3+c} \geq 2 sqrt{a+b+c}
sqrt{a^3 + a} + sqrt{b^3+b} + sqrt{c^3+c} \geq 2 sqrt{a+b+c}
Source: Iran TST 2008
May 25, 2008
inequalities
function
Iran
three variable inequality
Problem Statement
Let
a
,
b
,
c
>
0
a,b,c > 0
a
,
b
,
c
>
0
and
a
b
+
b
c
+
c
a
=
1
ab+bc+ca = 1
ab
+
b
c
+
c
a
=
1
. Prove that:
a
3
+
a
+
b
3
+
b
+
c
3
+
c
≥
2
a
+
b
+
c
.
\sqrt {a^3 + a} + \sqrt {b^3 + b} + \sqrt {c^3 + c}\geq2\sqrt {a + b + c}.
a
3
+
a
+
b
3
+
b
+
c
3
+
c
≥
2
a
+
b
+
c
.
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