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National and Regional Contests
Canada Contests
Canada National Olympiad
1996 Canada National Olympiad
2
System of equations
System of equations
Source: Canada 1996
March 4, 2006
function
inequalities
algebra unsolved
algebra
Problem Statement
Find all real solutions to the following system of equations. Carefully justify your answer.
{
4
x
2
1
+
4
x
2
=
y
4
y
2
1
+
4
y
2
=
z
4
z
2
1
+
4
z
2
=
x
\left\{ \begin{array}{c} \displaystyle\frac{4x^2}{1+4x^2} = y \\ \\ \displaystyle\frac{4y^2}{1+4y^2} = z \\ \\ \displaystyle\frac{4z^2}{1+4z^2} = x \end{array} \right.
⎩
⎨
⎧
1
+
4
x
2
4
x
2
=
y
1
+
4
y
2
4
y
2
=
z
1
+
4
z
2
4
z
2
=
x
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