13.087. A positive integer is thought of. The digit 5 is appended to its right, and from the resulting new number, the square of the thought number is subtracted. The difference is divided by the thought number, and then the thought number is subtracted, and the result is one. What number is thought of?
## Solution.

Let $x$ be the number thought of. Then the new number can be represented as $10 x + 5$. According to the condition, $\frac{10 x + 5 - x^2}{x} - x = 1$, from which $x = 5$.

Answer: 5.

![](https://cdn.mathpix.com/cropped/2024_05_22_fa9db84b44b98ec0a5c7g-847.jpg?height=426&width=608&top_left_y=1379&top_left_x=112)

Fig. 13.6