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Germany Contests
German National Olympiad
2000 German National Olympiad
4
\sqrt{x+y}+\sqrt{z} = 7, \sqrt{x+z}+\sqrt{y} = 7,\sqrt{y+z}+\sqrt{x} = 5
\sqrt{x+y}+\sqrt{z} = 7, \sqrt{x+z}+\sqrt{y} = 7,\sqrt{y+z}+\sqrt{x} = 5
Source: Germany 2000 p4
February 23, 2020
system of equations
algebra
Problem Statement
Find all nonnegative solutions
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
to the system
{
x
+
y
+
z
=
7
x
+
z
+
y
=
7
y
+
z
+
x
=
5
\begin{cases} \sqrt{x+y}+\sqrt{z} = 7 \\ \sqrt{x+z}+\sqrt{y} = 7 \\ \sqrt{y+z}+\sqrt{x} = 5 \end{cases}
⎩
⎨
⎧
x
+
y
+
z
=
7
x
+
z
+
y
=
7
y
+
z
+
x
=
5
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