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2017 NMTC Junior
6
Algebra problem
Algebra problem
Source: NMTC 2017 Juniors P6
October 28, 2017
algebra
Problem Statement
If
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are positive reals such that
a
2
+
b
2
=
c
2
+
d
2
a^2+b^2=c^2+d^2
a
2
+
b
2
=
c
2
+
d
2
and
a
2
+
d
2
−
a
d
=
b
2
+
c
2
+
b
c
a^2+d^2-ad=b^2+c^2+bc
a
2
+
d
2
−
a
d
=
b
2
+
c
2
+
b
c
, find the value of
a
b
+
c
d
a
d
+
b
c
\frac{ab+cd}{ad+bc}
a
d
+
b
c
ab
+
c
d
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