Question

x(в квадрате) + 2(a-b)x-4ab=0. решение полностью напишите.

Answer 1

1. X^2+(2A-2B)X-4AB=0

 2. X^2+2AX-2BX-4AB=0

Answer 2

Solution for the Equation x^2 + 2(a-b)x - 4ab = 0

To solve the quadratic equation x^2 + 2(a-b)x - 4ab = 0, we can use the quadratic formula:

Quadratic Formula: The solutions for the quadratic equation ax^2 + bx + c = 0 are given by: \[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \]

Applying the Quadratic Formula to the Given Equation

For the given equation x^2 + 2(a-b)x - 4ab = 0, we can identify the values of a, b, and c as follows: - a = 1 - b = 2(a-b) - c = -4ab

Now, we can substitute these values into the quadratic formula to find the solutions for x.

Substituting Values into the Quadratic Formula

Using the quadratic formula, the solutions for x are given by: \[ x = \frac{{-2(a-b) \pm \sqrt{{(2(a-b))^2 - 4*1*(-4ab)}}}}{{2*1}} \]

Simplifying the expression under the square root: \[ x = \frac{{-2(a-b) \pm \sqrt{{4(a-b)^2 + 16ab}}}}{{2}} \]

Final Solutions

Therefore, the solutions for the given quadratic equation x^2 + 2(a-b)x - 4ab = 0 are: \[ x = \frac{{-2(a-b) \pm \sqrt{{4(a-b)^2 + 16ab}}}}{{2}} \]

This provides the general solutions for the given quadratic equation.