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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2006 China Second Round Olympiad
3
solve the system of equations
solve the system of equations
Source: China second round 2006 p3
March 10, 2012
algebra
system of equations
algebra unsolved
Problem Statement
Solve the system of equations in real numbers:
{
x
−
y
+
z
−
w
=
2
x
2
−
y
2
+
z
2
−
w
2
=
6
x
3
−
y
3
+
z
3
−
w
3
=
20
x
4
−
y
4
+
z
4
−
w
4
=
66
\begin{cases} x-y+z-w=2 \\ x^2-y^2+z^2-w^2=6 \\ x^3-y^3+z^3-w^3=20 \\ x^4-y^4+z^4-w^4=66 \end{cases}
⎩
⎨
⎧
x
−
y
+
z
−
w
=
2
x
2
−
y
2
+
z
2
−
w
2
=
6
x
3
−
y
3
+
z
3
−
w
3
=
20
x
4
−
y
4
+
z
4
−
w
4
=
66
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