Question

Найдите наибольший отрицательный корень уравнения cosx+cos(2x)= 2. Ответ запишите в градусах.

Answer 1

Cosx+2cos²x-1-2=0
2cos²x+cosx-3=0
cosx=a
2a+a-3=0
D=1+24=25
a1=(-1-5)/4=-1,5⇒cosx=-1,5∉[-1;1]
a2=(-1+5)/4=1⇒cosx=1⇒x=2πn
Ответ х=-2π

Answer 2

Solving the Equation \( \cos(x) \cdot \cos(2x) = 2 \)

To find the largest negative root of the equation \( \cos(x) \cdot \cos(2x) = 2 \) and express the answer in degrees, we can use the given search results to solve the equation.

The equation \( \cos(x) \cdot \cos(2x) = 2 \) can be rewritten as \( \cos(x) \cdot (2\cos^2(x) - 1) = 2 \).

By substituting \( \cos(x) = y \), the equation becomes a quadratic equation in \( y \), which can be solved to find the values of \( y \).

Solution Steps:

1. Rewrite the equation \( \cos(x) \cdot \cos(2x) = 2 \) as \( \cos(x) \cdot (2\cos^2(x) - 1) = 2 \). 2. Substitute \( \cos(x) = y \) to convert the equation into a quadratic equation in \( y \). 3. Solve the quadratic equation to find the values of \( y \). 4. Convert the values of \( y \) back to \( x \) and find the largest negative root.

Solution:

The given search results do not directly provide the solution to the equation \( \cos(x) \cdot \cos(2x) = 2 \). Therefore, I will use the standard method to solve the equation.

The equation \( \cos(x) \cdot (2\cos^2(x) - 1) = 2 \) can be solved using trigonometric identities and algebraic manipulation. After solving the equation, the largest negative root in degrees can be determined.

Let's proceed with solving the equation using the standard method to find the largest negative root in degrees.