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Moldova Team Selection Test
2020 Moldova Team Selection Test
2
Interesting inequality
Interesting inequality
Source: Moldova TST 2020
March 7, 2020
Inequality
inequalities
Problem Statement
Show that for any positive real numbers
a
a
a
,
b
b
b
,
c
c
c
the following inequality takes place
a
b
+
b
c
+
c
a
+
a
+
b
+
c
a
2
+
b
2
+
c
2
≥
3
+
3
\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{a+b+c}{\sqrt{a^2+b^2+c^2}} \geq 3+\sqrt{3}
b
a
+
c
b
+
a
c
+
a
2
+
b
2
+
c
2
a
+
b
+
c
≥
3
+
3
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