Question

3 cos^2х - 5cosx -2=0.​

Answer 1

Ответ:

Пошаговое объяснение:

3*cos^2x-5cosx-2=0

Пусть cos x=t, получаем квадратное уравнение 3t^2-5t-2=0

Дискриминант D=25+4*2*3=49

t=(5+7)/6=2 или t=(5-7)/6=-1/3

Получаем: cosx=2 или cosx=-1/3

У первого уравнения решений нет,

cos x=-1/3

x=arccos(-1/3) или х=pi-arccos(-1/3)

Answer 2

To solve the quadratic equation $3\cos^2(x) - 5\cos(x) - 2 = 0$, we can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this equation, $a = 3$, $b = -5$, and $c = -2$. Plugging these values into the formula, we get:

$x = \frac{5 \pm \sqrt{(-5)^2 - 4 \cdot 3 \cdot (-2)}}{2 \cdot 3}$ $x = \frac{5 \pm \sqrt{25 + 24}}{6}$ $x = \frac{5 \pm \sqrt{49}}{6}$ $x = \frac{5 \pm 7}{6}$

So, we have two possible solutions for $x$:

1. $x = \frac{5 + 7}{6} = \frac{12}{6} = 2$
2. $x = \frac{5 - 7}{6} = \frac{-2}{6} = -\frac{1}{3}$

Therefore, the solutions to the equation $3\cos^2(x) - 5\cos(x) - 2 = 0$ are $x = 2$ and $x = -\frac{1}{3}$.