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Morocco Contests
Morocco National Olympiad
2011 Morocco National Olympiad
3
System
System
Source:
April 24, 2011
linear algebra
matrix
algebra unsolved
algebra
Problem Statement
Solve in
R
3
\mathbb{R}^{3}
R
3
the following system
{
x
2
−
y
=
z
−
1
y
2
−
z
=
x
−
1
z
2
−
x
=
y
−
1
\left\{\begin{matrix} \sqrt{x^{2}-y}=z-1\\ \sqrt{y^{2}-z}=x-1\\ \sqrt{z^{2}-x}=y-1 \end{matrix}\right.
⎩
⎨
⎧
x
2
−
y
=
z
−
1
y
2
−
z
=
x
−
1
z
2
−
x
=
y
−
1
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