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1950 Poland - Second Round
1
x^2+x+y=8, y^2+2xy+z=168, z^2+2yz+2xz=12480
x^2+x+y=8, y^2+2xy+z=168, z^2+2yz+2xz=12480
Source: Polish MO Second Round 1950 p1
September 1, 2024
algebra
system of equations
System
Problem Statement
Solve the system of equations
{
x
2
+
x
+
y
=
8
y
2
+
2
x
y
+
z
=
168
z
2
+
2
y
z
+
2
x
z
=
12480
\begin{cases} x^2+x+y=8\\ y^2+2xy+z=168\\ z^2+2yz+2xz=12480 \end{cases}
⎩
⎨
⎧
x
2
+
x
+
y
=
8
y
2
+
2
x
y
+
z
=
168
z
2
+
2
yz
+
2
x
z
=
12480
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