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Baltic Way
2014 Baltic Way
5
5
Part of
2014 Baltic Way
Problems
(1)
Possible values of an expression
Source: Baltic Way 2014, Problem 5
11/11/2014
Given positive real numbers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
that satisfy equalities
a
2
+
d
2
−
a
d
=
b
2
+
c
2
+
b
c
and
a
2
+
b
2
=
c
2
+
d
2
a^2 + d^2 - ad = b^2 + c^2 + bc \ \ \text{and} \ \ a^2 + b^2 = c^2 + d^2
a
2
+
d
2
−
a
d
=
b
2
+
c
2
+
b
c
and
a
2
+
b
2
=
c
2
+
d
2
find all possible values of the expression
a
b
+
c
d
a
d
+
b
c
.
\frac{ab+cd}{ad+bc}.
a
d
+
b
c
ab
+
c
d
.
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