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Problems
Contests
International Contests
Pan African
2000 Pan African
1
System of equations
System of equations
Source: Pan African 2000
October 3, 2005
inequalities
Problem Statement
Let
a
a
a
,
b
b
b
and
c
c
c
be real numbers such that
a
2
+
b
2
=
c
2
a^2+b^2=c^2
a
2
+
b
2
=
c
2
, solve the system:
z
2
=
x
2
+
y
2
z^2=x^2+y^2
z
2
=
x
2
+
y
2
(
z
+
c
)
2
=
(
x
+
a
)
2
+
(
y
+
b
)
2
(z+c)^2=(x+a)^2+(y+b)^2
(
z
+
c
)
2
=
(
x
+
a
)
2
+
(
y
+
b
)
2
in real numbers
x
,
y
x, y
x
,
y
and
z
z
z
.
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