Решите уравнение: 2x^2-4*корень из 2*x+3=0.

Ответ:

\[2x² - 4\sqrt{2}x + 3 = 0\]

\[D = \left( - 4\sqrt{2} \right)^{2} - 4 \cdot 2 \cdot 3 =\]

\[= 16 \cdot 2 - 24 = 32 - 24 = 8\]

\[x_{1} = \frac{4\sqrt{2} + \sqrt{8}}{2 \cdot 2} = \frac{4\sqrt{2} + 2\sqrt{2}}{4} =\]

\[= \frac{6\sqrt{2}}{4} = \frac{3\sqrt{2}}{2}\]

\[x_{2} = \frac{4\sqrt{2} - \sqrt{8}}{2 \cdot 2} = \frac{4\sqrt{2} - 2\sqrt{2}}{4} =\]

\[= \frac{2\sqrt{2}}{4} = \frac{\sqrt{2}}{2}\]

\[Ответ:x = \frac{3\sqrt{2}}{2};\ x = \frac{\sqrt{2}}{2}.\]