IMO Shortlist 1989 problem 26
Dodao/la:
arhiva2. travnja 2012. Let
![n \in \mathbb{Z}^+](/media/m/3/e/f/3eff91dca819e27aaedef5ae8072ead3.png)
and let
![a, b \in \mathbb{R}.](/media/m/a/e/1/ae15edfa0ee7bef1b42fcef3da23d8da.png)
Determine the range of
![x_0](/media/m/2/8/d/28d8bab97393896fe23acb973f7cb207.png)
for which
where
![x_0, x_1, \ldots , x_n](/media/m/f/a/f/faf0d69fb8f40d9a409488793e12e931.png)
are real variables.
%V0
Let $n \in \mathbb{Z}^+$ and let $a, b \in \mathbb{R}.$ Determine the range of $x_0$ for which
$$\sum^n_{i=0} x_i = a \text{ and } \sum^n_{i=0} x^2_i = b,$$
where $x_0, x_1, \ldots , x_n$ are real variables.
Izvor: Međunarodna matematička olimpijada, shortlist 1989