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Problems
Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2009 Korea Junior Math Olympiad
6
6
Part of
2009 Korea Junior Math Olympiad
Problems
(1)
1<\frac{b}{ab+b+1}+\frac{c}{bc+c+1}+\frac{d}{cd+d+1}+\frac{a}{da+a+1}<2
Source: KJMO 2009 p6
5/2/2019
If positive reals
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
satisfy
a
b
c
d
=
1.
abcd = 1.
ab
c
d
=
1.
Prove the following inequality
1
<
b
a
b
+
b
+
1
+
c
b
c
+
c
+
1
+
d
c
d
+
d
+
1
+
a
d
a
+
a
+
1
<
2.
1<\frac{b}{ab+b+1}+\frac{c}{bc+c+1}+\frac{d}{cd+d+1}+\frac{a}{da+a+1}<2.
1
<
ab
+
b
+
1
b
+
b
c
+
c
+
1
c
+
c
d
+
d
+
1
d
+
d
a
+
a
+
1
a
<
2.
inequalities
algebra
four variables
Inequality