Question

решите уравнение 9х2 + 12х + 1 = 0​

Answer 1

Ответ:

$x_{1} = \frac{-2 + \sqrt{3} }{3}$

$x_{2} = \frac{-2 - \sqrt{3} }{3}$

Объяснение:

$9x^{2} + 12x + 1 = 0\\D = b^{2} - 4ac = 144 - 4 * 9 * 1 = 144 - 36 = 108$

$x_{1} = \frac{-b + \sqrt{D} }{2a} = \frac{-12 + \sqrt{108} }{2 * 9} = \frac{-6 * 2 + 6\sqrt{3} }{2 * 9} = \frac{2 * 3(-2 + \sqrt{3} )}{2 * 3 * 3} = \frac{-2 + \sqrt{3} }{3}$

$x_{2} = \frac{-b - \sqrt{D} }{2a} = \frac{-12 - \sqrt{108} }{2 * 9} = \frac{-6 * 2 - 6\sqrt{3} }{2 * 9} = \frac{2 * 3(-2 - \sqrt{3} )}{2 * 3 * 3} = \frac{-2 - \sqrt{3} }{3}$

Answer 2

Ответ:

$\frac{-2 - \sqrt{3}}{3}; \frac{-2 + \sqrt{3}}{3}$

Объяснение:

9x² + 12x + 1 = 0

D = 144 - 9*4 = 144 - 36 = 108. √D = √108 = 6√3

x₁ = (-12 - 6√3) / 18 = (-2 - √3) /

x₂ = (-12 + 6√3) / 18 = (-2 + √3) / 3

$Otvet:\frac{-2 - \sqrt{3}}{3}; \frac{-2 + \sqrt{3}}{3}$