MathDB
Problems
Contests
National and Regional Contests
Germany Contests
QEDMO
2005 QEDMO 1st
12 (U2)
12 (U2)
Part of
2005 QEDMO 1st
Problems
(1)
Fear this inequality! [(b+c)^2 / (a^2+bc) + ... >= 6]
Source: problem 12 (U2) of QEDMO 1; created by Peter Scholze and me
11/7/2005
For any three positive real numbers
a
a
a
,
b
b
b
,
c
c
c
, prove the inequality
(
b
+
c
)
2
a
2
+
b
c
+
(
c
+
a
)
2
b
2
+
c
a
+
(
a
+
b
)
2
c
2
+
a
b
≥
6.
\frac{\left(b+c\right)^{2}}{a^{2}+bc}+\frac{\left(c+a\right)^{2}}{b^{2}+ca}+\frac{\left(a+b\right)^{2}}{c^{2}+ab}\geq 6.
a
2
+
b
c
(
b
+
c
)
2
+
b
2
+
c
a
(
c
+
a
)
2
+
c
2
+
ab
(
a
+
b
)
2
≥
6.
Darij
inequalities
function
inequalities proposed