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2020 IMO Shortlist
A3
A3
Part of
2020 IMO Shortlist
Problems
(1)
Minimizing simple sum of fractions
Source: ISL 2020 A3
7/20/2021
Suppose that
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are positive real numbers satisfying
(
a
+
c
)
(
b
+
d
)
=
a
c
+
b
d
(a+c)(b+d)=ac+bd
(
a
+
c
)
(
b
+
d
)
=
a
c
+
b
d
. Find the smallest possible value of
a
b
+
b
c
+
c
d
+
d
a
.
\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}.
b
a
+
c
b
+
d
c
+
a
d
.
Israel
algebra
Inequality
IMO Shortlist
IMO Shortlist 2020
4-variable inequality
inequalities