Question

1024+4^2x-5*4 ^x+2=0

Answer 1

1024+8х-20х+2=0
1026-12х=0
-12х=0-1026
-12х=1026
х=1026/-12 или 85.5

Answer 2

To solve the equation 1024 + 4^(2x) - 5 * 4^x + 2 = 0, we can follow these steps:

1. Let's simplify the equation by substituting a variable. Let's say u = 4^x. The equation becomes: 1024 + u^2 - 5u + 2 = 0.

2. Rearrange the equation: u^2 - 5u + 1026 = 0.

3. Now we have a quadratic equation in terms of u. To solve it, we can either factor it or use the quadratic formula.

   Using the quadratic formula: The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using: x = (-b ± √(b^2 - 4ac)) / (2a).

   In our equation u^2 - 5u + 1026 = 0, a = 1, b = -5, and c = 1026. Plugging these values into the quadratic formula:

   u = (-(-5) ± √((-5)^2 - 4(1)(1026))) / (2(1)) = (5 ± √(25 - 4104)) / 2 = (5 ± √(-4079)) / 2

   Since the discriminant (√(-4079)) is negative, the quadratic equation does not have real solutions. Therefore, there are no real solutions for the equation 1024 + 4^(2x) - 5 * 4^x + 2 = 0.