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Moscow Mathematical Olympiad
1935 Moscow Mathematical Olympiad
010
MMO 010 Moscow MO 1935 3 variable parameter system of equations
MMO 010 Moscow MO 1935 3 variable parameter system of equations
Source:
July 17, 2019
system of equations
algebra
parameter
Problem Statement
Solve the system
{
x
2
+
y
2
−
2
z
2
=
2
a
2
x
+
y
+
2
z
=
4
(
a
2
+
1
)
z
2
−
x
y
=
a
2
\begin{cases} x^2 + y^2 - 2z^2 = 2a^2 \\ x + y + 2z = 4(a^2 + 1) \\ z^2 - xy = a^2 \end{cases}
⎩
⎨
⎧
x
2
+
y
2
−
2
z
2
=
2
a
2
x
+
y
+
2
z
=
4
(
a
2
+
1
)
z
2
−
x
y
=
a
2
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