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Poland - Second Round
1964 Poland - Second Round
4
4
Part of
1964 Poland - Second Round
Problems
(1)
(z - x)(x - y) = a, (x - y)(y - z) = b, (y - z)(z - x) = c
Source: Polish MO Second Round 1964 p4
8/31/2024
Find the real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
satisfying the system of equations
(
z
−
x
)
(
x
−
y
)
=
a
(z - x)(x - y) = a
(
z
−
x
)
(
x
−
y
)
=
a
(
x
−
y
)
(
y
−
z
)
=
b
(x - y)(y - z) = b
(
x
−
y
)
(
y
−
z
)
=
b
(
y
−
z
)
(
z
−
x
)
=
c
(y - z)(z - x) = c
(
y
−
z
)
(
z
−
x
)
=
c
where
a
,
b
,
c
a, b, c
a
,
b
,
c
are given real numbers.
algebra
system of equations
System