Решите уравнение: x^2+x^2/|x| -6=0.

Ответ:

\[x² + \frac{x^{2}}{|x|} - 6 = 0\]

\[x > 0\]

\[x^{2} + \frac{x^{2}}{x} - 6 = 0\]

\[x² + x - 6 = 0\ \]

\[D = b^{2} - 4ac =\]

\[= 1 - 4 \cdot 1 \cdot ( - 6) =\]

\[= 1 + 24 = 25\]

\[x_{1} = \frac{- 1 - 5}{2} = - \frac{6}{2} = - 3 \Longrightarrow\]

\[\Longrightarrow не\ подходит,\ x > 0\]

\[x_{2} = \frac{- 1 + 5}{2} = \frac{4}{2} = 2\]

\[x < 0\]

\[x^{2} + \frac{x^{2}}{- x} - 6 = 0\]

\[x² - x - 6 = 0\]

\[D = b^{2} - 4ac =\]

\[= 1 - 4 \cdot 1 \cdot ( - 6) = 1 + 24 = 25\]

\[x_{1} = \frac{1 - 5}{2} = - \frac{4}{2} = - 2\]

\[x_{2} = \frac{1 + 5}{2} = \frac{6}{2} = 3 \Longrightarrow\]

\[\Longrightarrow не\ подходит,\ x < 0\]

\[Ответ:x_{1} = - 2;\ \ x_{2} = 2.\]