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Moldova Team Selection Test
1999 Moldova Team Selection Test
5
5
Part of
1999 Moldova Team Selection Test
Problems
(1)
$$\sqrt{x+a_1}+\sqrt{x+a_2}+\ldots+\sqrt{x+a_n}=n\sqrt{x}$$
Source: Moldova TST 1999
8/7/2023
Let
a
1
,
a
2
,
…
,
a
n
a_1, a_2, \ldots, a_n
a
1
,
a
2
,
…
,
a
n
be real numbers, but not all of them null. Show that the equation
x
+
a
1
+
x
+
a
2
+
…
+
x
+
a
n
=
n
x
\sqrt{x+a_1}+\sqrt{x+a_2}+\ldots+\sqrt{x+a_n}=n\sqrt{x}
x
+
a
1
+
x
+
a
2
+
…
+
x
+
a
n
=
n
x
has at most one real solution.
equation