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National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2006 Korea Junior Math Olympiad
6
6
Part of
2006 Korea Junior Math Olympiad
Problems
(1)
\frac{a + b + c + d}{(1 + a^2)(1 + b^2)(1 + c^2)(1 + d^2)}< 1
Source: KJMO 2006 p6
5/1/2019
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
algebra
inequalities
four variables