Question

Решите уравнение(2x-3)^2-(1-2x)^2=4

Answer 1

$(2x-3)^2-(1-2x)^2=4\\4x^2-12x+9-(1-4x+4x^2)=4\\4x^2-12x+9-1+4x-4x^2=4\\-8x=4-8\\-8x=-4\\x=0.5$

Answer 2

(2x-3)^2-(1-2x)^2=4

(2x-3-1+2x)(2x-3+1-2x)=4

4(4x-4)=4

4x-4=1

4x=5

x=5/4

Answer 3

To solve the equation (2x-3)^2 - (1-2x)^2 = 4, follow these steps:

Step 1: Expand the squared terms on both sides of the equation. Step 2: Simplify the equation by combining like terms. Step 3: Solve for x.

Let's go through each step:

Step 1: Expand the squared terms.

(2x-3)^2 = (2x-3)(2x-3) = 4x^2 - 12x + 9 (1-2x)^2 = (1-2x)(1-2x) = 1 - 2x - 2x + 4x^2 = 4x^2 - 4x + 1

Step 2: Simplify the equation.

(4x^2 - 12x + 9) - (4x^2 - 4x + 1) = 4 Now, let's remove the parentheses by distributing the negative sign on the right side.

4x^2 - 12x + 9 - 4x^2 + 4x - 1 = 4

Step 3: Combine like terms and bring the constant term to one side of the equation.

4x^2 - 4x^2 - 12x + 4x + 9 - 1 = 4

Simplify the equation further:

-8x + 8 = 4

Now, isolate the term with x:

-8x = 4 - 8

-8x = -4

Finally, solve for x:

x = (-4)/(-8)

x = 1/2

Therefore, the solution to the equation is x = 1/2.