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Russia Contests
Moscow Mathematical Olympiad
1957 Moscow Mathematical Olympiad
366
366
Part of
1957 Moscow Mathematical Olympiad
Problems
(1)
MMO 366 Moscow MO 1957 system 3x3 .. 2x_1^2/(1+x_1^2)=x_2
Source:
3/20/2021
Solve the system:
{
2
x
1
2
1
+
x
1
2
=
x
2
2
x
2
2
1
+
x
2
2
=
x
3
2
x
3
2
1
+
x
3
2
=
x
1
\begin{cases} \dfrac{2x_1^2}{1+x_1^2}=x_2 \\ \\ \dfrac{2x_2^2}{1+x_2^2}=x_3\\ \\ \dfrac{2x_3^2}{1+x_3^2}=x_1\end{cases}
⎩
⎨
⎧
1
+
x
1
2
2
x
1
2
=
x
2
1
+
x
2
2
2
x
2
2
=
x
3
1
+
x
3
2
2
x
3
2
=
x
1
algebra
system of equations