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Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2010 Junior Balkan Team Selection Tests - Moldova
5
a/(a+b) x (a+2b)/(a+3b) < \sqrt{ a /(a+4b)}
a/(a+b) x (a+2b)/(a+3b) < \sqrt{ a /(a+4b)}
Source: 2010 Moldova JBMO TST p5
February 25, 2021
inequalities
Problem Statement
For any strictly positive numbers
a
a
a
and
b
b
b
, prove the inequality
a
a
+
b
⋅
a
+
2
b
a
+
3
b
<
a
a
+
4
b
.
\frac{a}{a+b} \cdot \frac{a+2b}{a+3b} < \sqrt{ \frac{a}{a+4b}}.
a
+
b
a
⋅
a
+
3
b
a
+
2
b
<
a
+
4
b
a
.
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