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National and Regional Contests
Morocco Contests
Morocco National Olympiad
2011 Morocco National Olympiad
2
Moroccan MO
Moroccan MO
Source:
April 30, 2011
linear algebra
matrix
inequalities
algebra
polynomial
algebra unsolved
Problem Statement
Solve in
(
R
+
∗
)
4
(\mathbb{R}_{+}^{*})^{4}
(
R
+
∗
)
4
the following system :
{
x
+
y
+
z
+
t
=
4
1
x
+
1
y
+
1
z
+
1
t
=
5
−
1
x
y
z
t
\left\{\begin{matrix} x+y+z+t=4\\ \frac{1}{x}+\frac{1}{y}+\frac{1}{z}+\frac{1}{t}=5-\frac{1}{xyzt} \end{matrix}\right.
{
x
+
y
+
z
+
t
=
4
x
1
+
y
1
+
z
1
+
t
1
=
5
−
x
yz
t
1
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