Рациональные уравнения. Задача 2

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

Ответ

ОТВЕТ: -0,2; 0,5.

Решение

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

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

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