MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey MO (2nd round)
2005 Turkey MO (2nd round)
1
a,b,c,d radical inequality
a,b,c,d radical inequality
Source:
November 1, 2010
inequalities
inequalities proposed
Problem Statement
For all positive real numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
prove the inequality
a
4
+
c
4
+
a
4
+
d
4
+
b
4
+
c
4
+
b
4
+
d
4
≥
2
2
(
a
d
+
b
c
)
\sqrt{a^4+c^4}+\sqrt{a^4+d^4}+\sqrt{b^4+c^4}+\sqrt{b^4+d^4} \ge 2\sqrt{2}(ad+bc)
a
4
+
c
4
+
a
4
+
d
4
+
b
4
+
c
4
+
b
4
+
d
4
≥
2
2
(
a
d
+
b
c
)
Back to Problems
View on AoPS