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Israel Team Selection Test
2016 Israel Team Selection Test
1
Easy Asymmetric Inequality
Easy Asymmetric Inequality
Source: Israel Autumn TST1/1
October 2, 2016
inequalities
calculus
lagrange
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive numbers satisfying
a
b
+
b
c
+
c
a
+
2
a
b
c
=
1
ab+bc+ca+2abc=1
ab
+
b
c
+
c
a
+
2
ab
c
=
1
. Prove that
4
a
+
b
+
c
≥
2
4a+b+c \geq 2
4
a
+
b
+
c
≥
2
.
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