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

To solve the equation (2-x)(2x+1) = (2+x)(x-2), we need to find the value(s) of 'x' that satisfy the equation. Let's go step by step:

Step 1: Expand both sides of the equation.

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

Step 2: Apply the distributive property (FOIL) to expand both sides.

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

Simplify each side:

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

Step 3: Bring all the terms to one side of the equation to set it equal to zero:

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

Step 4: Combine like terms:

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

Step 5: Combine the x^2 terms:

-2x^2 - x^2 = -3x^2

Step 6: Combine the x terms:

4x - x + 2x = 5x

Step 7: Now our equation becomes:

-3x^2 + 5x + 4 = 0

This is a quadratic equation in the standard form (ax^2 + bx + c = 0), where a = -3, b = 5, and c = 4.

Step 8: To solve the quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values, we get:

x = (-(5) ± √(5^2 - 4(-3)(4))) / 2(-3) x = (-5 ± √(25 + 48)) / (-6) x = (-5 ± √73) / (-6)

So the two solutions for 'x' are:

1. x = (-5 + √73) / (-6)
2. x = (-5 - √73) / (-6)

Please note that these are approximate values since √73 is an irrational number. If you need decimal approximations, you can use a calculator to get more precise values.