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Caucasus Mathematical Olympiad
2015 Caucasus Mathematical Olympiad
1
solve (x-a)(x-b)=(x-c)(x-d) if a+d=b+c=2015, a \ne c
solve (x-a)(x-b)=(x-c)(x-d) if a+d=b+c=2015, a \ne c
Source: Caucasus 2015 10.1
April 26, 2019
algebra
equation
Problem Statement
Find the roots of the equation
(
x
−
a
)
(
x
−
b
)
=
(
x
−
c
)
(
x
−
d
)
(x-a)(x-b)=(x-c)(x-d)
(
x
−
a
)
(
x
−
b
)
=
(
x
−
c
)
(
x
−
d
)
, if you know that
a
+
d
=
b
+
c
=
2015
a+d=b+c=2015
a
+
d
=
b
+
c
=
2015
and
a
≠
c
a \ne c
a
=
c
(numbers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
are not given).
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