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1989 Greece National Olympiad
1
\sqrt{9+x_1}+ \sqrt{9+x_2}+...+ \sqrt{9+x_{100}}=100\sqrt{10}
\sqrt{9+x_1}+ \sqrt{9+x_2}+...+ \sqrt{9+x_{100}}=100\sqrt{10}
Source: 1989 Greece MO Grade XII p1
September 6, 2024
algebra
system of equations
Problem Statement
Find all real solutions of
9
+
x
1
+
9
+
x
2
+
.
.
.
+
9
+
x
100
=
100
10
16
−
x
1
+
16
−
x
2
+
.
.
.
+
16
−
x
100
=
100
15
\begin{matrix} \sqrt{9+x_1}+ \sqrt{9+x_2}+...+ \sqrt{9+x_{100}}=100\sqrt{10}\\ \sqrt{16-x_1}+ \sqrt{16-x_2}+...+ \sqrt{16-x_{100}}=100\sqrt{15} \end{matrix}
9
+
x
1
+
9
+
x
2
+
...
+
9
+
x
100
=
100
10
16
−
x
1
+
16
−
x
2
+
...
+
16
−
x
100
=
100
15
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