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Balkan MO Shortlist
2016 Balkan MO Shortlist
A5
A5
Part of
2016 Balkan MO Shortlist
Problems
(1)
a+b+c+d=2 and ab+bc+cd+da+ac+bd = 0, find min, max of abcd
Source: Balkan BMO Shortlist 2016 A5
7/30/2019
Let
a
,
b
,
c
a, b,c
a
,
b
,
c
and
d
d
d
be real numbers such that
a
+
b
+
c
+
d
=
2
a + b + c + d = 2
a
+
b
+
c
+
d
=
2
and
a
b
+
b
c
+
c
d
+
d
a
+
a
c
+
b
d
=
0
ab + bc + cd + da + ac + bd = 0
ab
+
b
c
+
c
d
+
d
a
+
a
c
+
b
d
=
0
. Find the minimum value and the maximum value of the product
a
b
c
d
abcd
ab
c
d
.
algebra
system of equations
inequalities
minimum
maximum
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