Question

(2cos^2x-cosx)корень-cosx=0

Answer 1

Если я тебя правильно понял, то данное уравнение решается таким способом, расписанном в скриншоте, оба корня - особые случаи, их нужно знать.

 

Answer 2

To solve the equation (2cos^2x - cosx)√(cosx) = 0, we can follow these steps:

Step 1: Factor out common terms Let's factor out cosx from the equation: cosx(2cosx - 1)√(cosx) = 0

Step 2: Apply the zero product property According to the zero product property, if a product of factors is equal to zero, then at least one of the factors must be equal to zero. Therefore, we set each factor equal to zero and solve for x.

cosx = 0

To find the solutions for cosx = 0, we need to determine the values of x where cosx is equal to zero. In the unit circle, cosx is zero at x = π/2 + nπ, where n is an integer.

2cosx - 1 = 0

To solve this equation, we isolate the cosx term:

2cosx = 1 cosx = 1/2

The solutions for cosx = 1/2 are x = π/3 + 2nπ and x = 5π/3 + 2nπ, where n is an integer.

Step 3: Combine the solutions The solutions for cosx = 0 are x = π/2 + nπ, and the solutions for cosx = 1/2 are x = π/3 + 2nπ and x = 5π/3 + 2nπ.

Therefore, the combined solution set for the equation (2cos^2x - cosx)√(cosx) = 0 is: x = π/2 + nπ, π/3 + 2nπ, and 5π/3 + 2nπ, where n is an integer.