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Kvant 2019
M2550
M2550
Part of
Kvant 2019
Problems
(1)
Simple Inequality from Kvant
Source: Kvant 2019 No. 3, Problem M2550
4/23/2019
Let
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
be real numbers. Prove that
a
+
b
b
+
c
+
b
+
c
c
+
a
+
c
+
a
a
+
b
≥
2
a
+
2
b
+
2
c
\frac{a+b}{\sqrt{b+c}}+\frac{b+c}{\sqrt{c+a}}+\frac{c+a}{\sqrt{a+b}}\geq \sqrt{2a}+ \sqrt{2b}+ \sqrt{2c}
b
+
c
a
+
b
+
c
+
a
b
+
c
+
a
+
b
c
+
a
≥
2
a
+
2
b
+
2
c
Б. Кайрат (Казахстан), А. Храбров
inequalities
algebra
Kvant