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Moscow Mathematical Olympiad
1937 Moscow Mathematical Olympiad
032
MMO 032 Moscow MO 1937 x+y+z = a,x^2+y^2+z^2=a^2, x^3 +y^3+z^3=a^3
MMO 032 Moscow MO 1937 x+y+z = a,x^2+y^2+z^2=a^2, x^3 +y^3+z^3=a^3
Source:
July 18, 2019
algebra
system of equations
parameter
Problem Statement
Solve the system
{
x
+
y
+
z
=
a
x
2
+
y
2
+
z
2
=
a
2
x
3
+
y
3
+
z
3
=
a
3
\begin{cases} x+ y +z = a \\ x^2 + y^2 + z^2 = a^2 \\ x^3 + y^3 +z^3 = a^3 \end{cases}
⎩
⎨
⎧
x
+
y
+
z
=
a
x
2
+
y
2
+
z
2
=
a
2
x
3
+
y
3
+
z
3
=
a
3
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