Question

(2-x)(2x+1)=(2+x)(x-2)​ срочноооо

Answer 1

Решение:

$(2-x)(2x+1)=(2+x)(x-2)\\\\4x + 2 - 2x^2 - x = x^2 - 4\\\\-2x^2 - x^2 + 4x - x +2 + 4 = 0\\\\-3x^2 + 3x + 6 = 0 |: (-3)\\\\x^2 - x - 2 = 0\\\\(x+1)(x-2) = 0\\\\x_1 = -1\\\\x_2 = 2$

Answer 2

Let's solve the given equation step by step:

(2 - x)(2x + 1) = (2 + x)(x - 2)

Expand both sides of the equation:

4x + 2 - 2x^2 - x = 2x - 4 + x^2 - 2x

Now, let's combine like terms on each side:

On the left side: 4x - 2x^2 - x - 2 = 0

On the right side: 2x - 2x + x^2 - 4 = x^2 - 4

Now, move all terms to one side to set the equation to zero:

4x - 2x^2 - x - 2 - (x^2 - 4) = 0

Simplify further:

4x - 2x^2 - x - 2 - x^2 + 4 = 0

Combine like terms:

4x - 3x^2 + 2 = 0

The equation is now in standard quadratic form: ax^2 + bx + c = 0

Now, we need to solve for x. However, this is a quadratic equation. To solve it, we can either use factoring, completing the square, or the quadratic formula.

Since the equation doesn't seem to have obvious factors, let's use the quadratic formula:

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In our equation, a = -3, b = 4, and c = 2:

x = (-(4) ± √((4)^2 - 4(-3)(2))) / 2(-3) x = (-4 ± √(16 + 24)) / (-6) x = (-4 ± √40) / (-6) x = (-4 ± √(4 * 10)) / (-6) x = (-4 ± 2√10) / (-6)

Now, let's find the two possible values of x:

1. x = (-4 + 2√10) / (-6)
2. x = (-4 - 2√10) / (-6)

Now, we can simplify these solutions:

1. x = (2√10 - 4) / 6 ≈ 0.3588
2. x = (-2√10 - 4) / 6 ≈ -1.0255

So the two solutions to the equation are approximately x ≈ 0.3588 and x ≈ -1.0255.