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Tournament Of Towns
1985 Tournament Of Towns
(082) T3
(082) T3
Part of
1985 Tournament Of Towns
Problems
(1)
TOT 082 1985 Spring Train J3 (x+y)^3=z, (y+z)^3=x, (z+x)^3=y
Source:
8/24/2019
Find all real solutions of the system of equations
{
(
x
+
y
)
3
=
z
(
y
+
z
)
3
=
x
(
z
+
x
)
3
=
y
\begin{cases} (x + y) ^3 = z \\ (y + z) ^3 = x \\ ( z+ x) ^3 = y \end{cases}
⎩
⎨
⎧
(
x
+
y
)
3
=
z
(
y
+
z
)
3
=
x
(
z
+
x
)
3
=
y
(Based on an idea by A . Aho , J. Hop croft , J. Ullman )
algebra
system of equations