\[x² + \frac{x^{2}}{|x|} - 6 = 0\]
\[x > 0\]
\[x^{2} + \frac{x^{2}}{x} - 6 = 0\]
\[x² + x - 6 = 0\ \]
\[D = b^{2} - 4ac =\]
\[= 1 - 4 \cdot 1 \cdot ( - 6) =\]
\[= 1 + 24 = 25\]
\[x_{1} = \frac{- 1 - 5}{2} = - \frac{6}{2} = - 3 \Longrightarrow\]
\[\Longrightarrow не\ подходит,\ x > 0\]
\[x_{2} = \frac{- 1 + 5}{2} = \frac{4}{2} = 2\]
\[x < 0\]
\[x^{2} + \frac{x^{2}}{- x} - 6 = 0\]
\[x² - x - 6 = 0\]
\[D = b^{2} - 4ac =\]
\[= 1 - 4 \cdot 1 \cdot ( - 6) = 1 + 24 = 25\]
\[x_{1} = \frac{1 - 5}{2} = - \frac{4}{2} = - 2\]
\[x_{2} = \frac{1 + 5}{2} = \frac{6}{2} = 3 \Longrightarrow\]
\[\Longrightarrow не\ подходит,\ x < 0\]
\[Ответ:x_{1} = - 2;\ \ x_{2} = 2.\]