Question

4cosПx - 2 корень из 2 = 0

Answer 1

2сos2x-корень из 2 = 0

2cos3x=корень из 2

cos3x=корень из 2 / 2

3x=+-arccos корень из 2 /2 + 2пи n, n прин. z

3x=+-пи/4+2пи n, n прин. z

x=+-3пи/4+2пи n/3, n прин. z

Вроде так

Answer 2

To solve the equation 4cos(πx) - 2√2 = 0, we need to find the value(s) of x that satisfy the equation. Let's go through the steps to solve it:

Step 1: Add 2√2 to both sides of the equation to isolate the cosine term: 4cos(πx) = 2√2

Step 2: Divide both sides by 4 to isolate the cosine term on one side: cos(πx) = 2√2 / 4

Step 3: Simplify the right-hand side: cos(πx) = √2 / 2

Step 4: Now, we need to find the angles whose cosine is equal to √2 / 2. These angles are π/4 and 7π/4 in the unit circle.

Step 5: Set up equations for both possible angles:

1. πx = π/4
2. πx = 7π/4

Step 6: Solve for x in each equation:

1. x = π/4π = 1/4
2. x = 7π/4π = 7/4

So, the solutions to the equation 4cos(πx) - 2√2 = 0 are x = 1/4 and x = 7/4.