Question

256х^2+(х-1)^2=100(х^2-х)

Answer 1

Ответ:

↓

Пошаговое объяснение:

       49   2*\/ 561  

x1 = - --- - ---------

      157      157    

                _____

       49   2*\/ 561  

x2 = - --- + ---------

      157      157  

Answer 2

To solve the equation 256x^2 + (x - 1)^2 = 100(x^2 - x), you'll first need to simplify and then solve for the value of x. Here are the steps to do that:

1. Expand and simplify the equation: 256x^2 + (x^2 - 2x + 1) = 100x^2 - 100x

2. Combine like terms on both sides of the equation: 256x^2 + x^2 - 2x + 1 = 100x^2 - 100x

3. Now, subtract 100x^2 from both sides to isolate the x^2 terms on one side of the equation: 256x^2 + x^2 - 2x + 1 - 100x^2 + 100x = 0

4. Combine the x^2 terms and the x terms: 256x^2 + x^2 - 100x^2 - 2x + 100x + 1 = 0

5. Simplify further: (256x^2 + x^2 - 100x^2) + (-2x + 100x) + 1 = 0 (257x^2 - 99x) + (98x + 1) = 0

6. Combine like terms: 257x^2 - 99x + 98x + 1 = 0

7. Simplify the equation: 257x^2 - x + 1 = 0

Now, you have a quadratic equation in the form ax^2 + bx + c = 0. You can solve this using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 257, b = -1, and c = 1. Plug these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 257 * 1)) / (2 * 257)

x = (1 ± √(1 - 1028)) / 514

x = (1 ± √(1 - 1028)) / 514

Since the discriminant (the value inside the square root) is negative, there are no real solutions to this equation. The solutions will be complex numbers. You can simplify the expression under the square root as follows:

x = (1 ± √(-1027)) / 514

x = (1 ± √1027i) / 514

So, the solutions for x are:

x = (1 + √1027i) / 514 x = (1 - √1027i) / 514