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2008 JBMO Shortlist
4
x+y+z=2008, x^2+y^2+z^2=6024^2,1/x+1/y+1/z=1/2008
x+y+z=2008, x^2+y^2+z^2=6024^2,1/x+1/y+1/z=1/2008
Source: JBMO 2008 Shortlist A4
October 14, 2017
JBMO
algebra
system of equations
Problem Statement
Find all triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of real numbers that satisfy the system
{
x
+
y
+
z
=
2008
x
2
+
y
2
+
z
2
=
602
4
2
1
x
+
1
y
+
1
z
=
1
2008
\begin{cases} x + y + z = 2008 \\ x^2 + y^2 + z^2 = 6024^2 \\ \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{2008} \end{cases}
⎩
⎨
⎧
x
+
y
+
z
=
2008
x
2
+
y
2
+
z
2
=
602
4
2
x
1
+
y
1
+
z
1
=
2008
1
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