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2010 Mediterranean Mathematics Olympiad
1
Mediterranean M.C. 2010 Problem 1
Mediterranean M.C. 2010 Problem 1
Source:
July 12, 2010
algebra
system of equations
algebra proposed
Problem Statement
Real numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are given. Solve the system of equations (unknowns
x
,
y
,
z
,
u
)
x,y,z,u)
x
,
y
,
z
,
u
)
x
2
−
y
z
−
z
u
−
y
u
=
a
x^{2}-yz-zu-yu=a
x
2
−
yz
−
z
u
−
y
u
=
a
y
2
−
z
u
−
u
x
−
x
z
=
b
y^{2}-zu-ux-xz=b
y
2
−
z
u
−
ux
−
x
z
=
b
z
2
−
u
x
−
x
y
−
y
u
=
c
z^{2}-ux-xy-yu=c
z
2
−
ux
−
x
y
−
y
u
=
c
u
2
−
x
y
−
y
z
−
z
x
=
d
u^{2}-xy-yz-zx=d
u
2
−
x
y
−
yz
−
z
x
=
d
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