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Turkey Contests
Turkey MO (2nd round)
2005 Turkey MO (2nd round)
1
1
Part of
2005 Turkey MO (2nd round)
Problems
(1)
a,b,c,d radical inequality
Source:
11/1/2010
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
)
inequalities
inequalities proposed