Решите уравнение: 3x^2-5x*корень из (3)+6=0.

Ответ:

\[3x² - 5x\sqrt{3} + 6 = 0\]

\[3x^{2} - 5\sqrt{3}x + 6 = 0\]

\[D = \left( - 5\sqrt{3} \right)^{2} - 4 \cdot 3 \cdot 6 =\]

\[= 25 \cdot 3 - 72 = 75 - 72 = 3\]

\[x_{1} = \frac{5\sqrt{3} - \sqrt{3}}{2 \cdot 3} = \frac{4\sqrt{3}}{6} = \frac{2\sqrt{3}}{3}\]

\[x_{2} = \frac{5\sqrt{3} + \sqrt{3}}{2 \cdot 3} = \frac{6\sqrt{3}}{6} = \sqrt{3}\]

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