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2014 BMT Spring
P1
BMT 2014 Spring - Analysis P1
BMT 2014 Spring - Analysis P1
Source:
January 6, 2022
inequalities
Problem Statement
Suppose that
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are non-negative real numbers such that
a
2
+
b
2
+
c
2
+
d
2
=
2
a^2+b^2+c^2+d^2=2
a
2
+
b
2
+
c
2
+
d
2
=
2
and
a
b
+
b
c
+
c
d
+
d
a
=
1
ab+bc+cd+da=1
ab
+
b
c
+
c
d
+
d
a
=
1
. Find the maximum value of
a
+
b
+
c
+
d
a+b+c+d
a
+
b
+
c
+
d
and determine all equality cases.
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