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Korea Contests
Korea Junior Mathematics Olympiad
2006 Korea Junior Math Olympiad
6
\frac{a + b + c + d}{(1 + a^2)(1 + b^2)(1 + c^2)(1 + d^2)}< 1
\frac{a + b + c + d}{(1 + a^2)(1 + b^2)(1 + c^2)(1 + d^2)}< 1
Source: KJMO 2006 p6
May 1, 2019
algebra
inequalities
four variables
Problem Statement
For all reals
a
,
b
,
c
,
d
a, b, c,d
a
,
b
,
c
,
d
prove the following inequality:
a
+
b
+
c
+
d
(
1
+
a
2
)
(
1
+
b
2
)
(
1
+
c
2
)
(
1
+
d
2
)
<
1
\frac{a + b + c + d}{(1 + a^2)(1 + b^2)(1 + c^2)(1 + d^2)}< 1
(
1
+
a
2
)
(
1
+
b
2
)
(
1
+
c
2
)
(
1
+
d
2
)
a
+
b
+
c
+
d
<
1
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