MathDB
Problems
Contests
National and Regional Contests
Indonesia Contests
Indonesia MO Shortlist
2015 Indonesia MO Shortlist
A5
sum \sqrt{\frac{a}{b+c}+\frac{b}{c+a}} >=3
sum \sqrt{\frac{a}{b+c}+\frac{b}{c+a}} >=3
Source: Indonesia MO (INAMO) 2015 P7
September 14, 2018
inequalities
algebra
three variable inequality
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers. Prove that
a
b
+
c
+
b
c
+
a
+
b
c
+
a
+
c
a
+
b
+
c
a
+
b
+
a
b
+
c
≥
3
\sqrt{\frac{a}{b+c}+\frac{b}{c+a}}+\sqrt{\frac{b}{c+a}+\frac{c}{a+b}}+\sqrt{\frac{c}{a+b}+\frac{a}{b+c}}\ge 3
b
+
c
a
+
c
+
a
b
+
c
+
a
b
+
a
+
b
c
+
a
+
b
c
+
b
+
c
a
≥
3
Back to Problems
View on AoPS