MathDB
Problems
Contests
National and Regional Contests
Germany Contests
QEDMO
2006 QEDMO 3rd
11
11
Part of
2006 QEDMO 3rd
Problems
(1)
Sorry for this one: (a^2+2b^2)/(b+c) + ... >= 3/2 (a+b+c)
Source: 3rd QEDMO 2006, problem 11, by me
4/14/2006
Guess I should stop proposing problems at 2:00 AM, as this can lead to ones like this here: Let
a
a
a
,
b
b
b
,
c
c
c
be three positive reals. Prove the inequality
a
2
+
2
b
2
b
+
c
+
b
2
+
2
c
2
c
+
a
+
c
2
+
2
a
2
a
+
b
≥
3
2
(
a
+
b
+
c
)
\frac{a^2+2b^2}{b+c}+\frac{b^2+2c^2}{c+a}+\frac{c^2+2a^2}{a+b}\geq\frac32\left(a+b+c\right)
b
+
c
a
2
+
2
b
2
+
c
+
a
b
2
+
2
c
2
+
a
+
b
c
2
+
2
a
2
≥
2
3
(
a
+
b
+
c
)
.
inequalities