26. $n$ is a positive integer, $a, b$ are given real numbers, $x_{0}, x_{1}, \cdots, x_{n}$ are real variables,
$$
\sum_{i=0}^{n} x_{i}=a, \quad \sum_{i=0}^{n} x_{i}^{2}=b .
$$

Determine the range of variation for $x_{n}$.
26. By the Cauchy inequality,
$$
\left(\sum_{1=1}^{n} x_{1}\right)^{2} \leqslant n \sum_{1=1}^{n} x_{1}^{2} \text {. }
$$

Therefore, $\left(a-x_{0}\right)^{2} \leqslant n\left(b-x_{0}^{2}\right)$,
which means $(n+1) x_{0}^{2}-2 a x_{0}+a^{2}-n b \leqslant 0$.
The discriminant of this quadratic trinomial is
$$
D=4 n(n+1)\left(b-\frac{a^{2}}{n+1}\right) .
$$
(1) If $b\frac{a^{2}}{n+1}$, then
$$
\frac{a-\sqrt{\frac{D}{4}}}{n+1} \leqslant x_{0} \leqslant \frac{a+\sqrt{\frac{D}{4}}}{n+1} .
$$