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National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
1999 Switzerland Team Selection Test
4
4
Part of
1999 Switzerland Team Selection Test
Problems
(1)
\frac{4x^2}{1+4x^2}= y,\frac{4y^2}{1+4y^2}= z, \frac{4z^2}{1+4z^2}= x
Source: Switzerland - Swiss TST 1999 p4
2/19/2020
Find all real solutions
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of the system
{
4
x
2
1
+
4
x
2
=
y
4
y
2
1
+
4
y
2
=
z
4
z
2
1
+
4
z
2
=
x
\begin{cases}\dfrac{4x^2}{1+4x^2}= y\\ \\\dfrac{4y^2}{1+4y^2}= z\\ \\ \dfrac{4z^2}{1+4z^2}= x \end{cases}
⎩
⎨
⎧
1
+
4
x
2
4
x
2
=
y
1
+
4
y
2
4
y
2
=
z
1
+
4
z
2
4
z
2
=
x
system of equations
algebra