Решите уравнение: 3x^2+x^2/|x| -4=0.

Ответ:

\[3x² + \frac{x^{2}}{|x|} - 4 = 0\ \]

\[1)\ x > 0:\]

\[3x² + \frac{x^{2}}{x} - 4 = 0\ \]

\[3x^{2} + x - 4 = 0\]

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

\[= 1 - 4 \cdot 3 \cdot ( - 4) = 1 + 48 = 49\]

\[x_{1} = \frac{- 1 + 7}{6} = \frac{6}{6} = 1;\]

\[x_{2} = \frac{- 1 - 7}{6} = - \frac{8}{6} = - \frac{4}{3} =\]

\[= - 1\frac{1}{3} < 0\ (не\ подходит).\]

\[2)\ \ x < 0:\]

\[3x^{2} + \frac{x^{2}}{- x} - 4 = 0\]

\[3x² - x - 4 = 0\]

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

\[= 1 - 4 \cdot 3 \cdot ( - 4) = 1 + 48 =\]

\[= 49\]

\[x_{1} = \frac{1 + 7}{6} = \frac{8}{6} = \frac{4}{3} =\]

\[= 1\frac{1}{3} > 0\ (не\ подходит).\]

\[x_{2} = \frac{1 - 7}{6} = - \frac{6}{6} = - 1.\]

\[Ответ:x = 1;x = - 1.\]