Задача 2. Решите уравнение    \(\frac{1}{{{x^2}}} + \frac{3}{x} = 10\)

Ответ

ОТВЕТ: -0,2;   0,5.

Решение

\(\frac{1}{{{x^2}}} + \frac{3}{x} = 10\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\frac{{1 + 3x-10{x^2}}}{{{x^2}}} = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{1 + 3x-10{x^2} = 0,}\\{{x^2} \ne 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \)

\( \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{\left[ {\begin{array}{*{20}{c}}{x = \frac{1}{2},\,\,\,}\\{x = -\frac{1}{5},}\end{array}} \right.}\\{x \ne 0\,\,\,\,\,\,\,}\end{array}} \right.\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = \frac{1}{2},\,\,\,}\\{x = -\frac{1}{5}.}\end{array}} \right.\)

Ответ:  \(-\frac{1}{5};\;\;\frac{1}{2}.\)