2.8. Let $n>1$ be a natural number. Find all positive solutions of the equation $x^{n}-n x+n-1=0$.

## 2.3. Equations with Radicals

In problems $2.9-2.15$, it is assumed that the values of square roots are non-negative. We are interested only in the real roots of the equations.
2.8. A n s w e r: $x=1$. It is clear that

$$
x^{n}-n x+n-1=\left(1+x+\ldots+x^{n-1}-n\right)(x-1)
$$

If $x>1$, then $1+x+\ldots+x^{n-1}-n>0$, and if $0<x<1$, then $1+x+\ldots$ $\cdots+x^{n-1}-n<0$.