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Vietnam National Olympiad
1981 Vietnam National Olympiad
1
Solving a system of four equations in four variables.
Solving a system of four equations in four variables.
Source: Vietnam MO 1981 P4
March 17, 2011
algebra
system of equations
algebra unsolved
Problem Statement
Solve the system of equations
x
2
+
y
2
+
z
2
+
t
2
=
50
;
x^2 + y^2 + z^2 + t^2 = 50;
x
2
+
y
2
+
z
2
+
t
2
=
50
;
x
2
−
y
2
+
z
2
−
t
2
=
−
24
;
x^2 - y^2 + z^2 - t^2 = -24;
x
2
−
y
2
+
z
2
−
t
2
=
−
24
;
x
y
=
z
t
;
xy = zt;
x
y
=
z
t
;
x
−
y
+
z
−
t
=
0.
x - y + z - t = 0.
x
−
y
+
z
−
t
=
0.
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