B1 Calculate the number for which the following is true: if we add its reciprocal and divide the resulting sum by its opposite value, we get the value $-1.04$.






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B1. We write the equation $\frac{x+\frac{1}{x}}{-x}=-1.04$. Considering that $-1.04=-\frac{26}{25}$. We substitute and transform the equation to $x+\frac{1}{x}=\frac{26}{25} x$. We simplify the equation to the form: $x^{2}-25=0$, factorize it, and obtain the solutions 5 and -5.

![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-11.jpg?height=75&width=1685&top_left_y=425&top_left_x=228)

![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-11.jpg?height=80&width=1688&top_left_y=480&top_left_x=227)

Converting the decimal number to a fraction $-1.04=-\frac{26}{25} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ point

Transforming the equation to $x+\frac{1}{x}=\frac{26}{25} x \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-11.jpg?height=57&width=1685&top_left_y=651&top_left_x=228)

![](https://cdn.mathpix.com/cropped/2024_06_07_c987701c9bb62194911fg-11.jpg?height=48&width=1685&top_left_y=707&top_left_x=228)