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Turkey Team Selection Test
2014 Turkey Team Selection Test
3
Hard ineq
Hard ineq
Source: Turkey TST 2014 Day 2 Problem 6
March 12, 2014
inequalities
inequalities proposed
Problem Statement
Prove that for all all non-negative real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
with
a
2
+
b
2
+
c
2
=
1
a^2+b^2+c^2=1
a
2
+
b
2
+
c
2
=
1
a
+
b
+
a
+
c
+
b
+
c
≥
5
a
b
c
+
2.
\sqrt{a+b}+\sqrt{a+c}+\sqrt{b+c} \geq 5abc+2.
a
+
b
+
a
+
c
+
b
+
c
≥
5
ab
c
+
2.
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