Question

(2x -3) 2 в степени-2x=9

Answer 1

(2x-3)²-2x-9=0
4x²-6x+9-2x-9=0
4x²-8x=0
4x(x-2)=0
x1=0; x2=2

Answer 2

Надеюсь,что так. Если что-то непонятно, напиши мне, напишу понятнее. Удачи!

Answer 3

To solve the equation (2x - 3)^2 * 2^(-2x) = 9, we'll go step by step.

Step 1: Expand the square term (2x - 3)^2. (2x - 3)^2 = (2x - 3) * (2x - 3) = 4x^2 - 6x - 6x + 9 = 4x^2 - 12x + 9.

Step 2: Rewrite 2^(-2x) as (1/2)^(2x). 2^(-2x) = (1/2)^(2x).

Now the equation becomes: (4x^2 - 12x + 9) * (1/2)^(2x) = 9.

Step 3: Multiply both sides by 2^(2x) to get rid of the fraction. (4x^2 - 12x + 9) = 9 * 2^(2x).

Step 4: Move all terms to one side of the equation. (4x^2 - 12x) = 9 * 2^(2x) - 9.

Step 5: Factor out 4 from the left side of the equation. 4(x^2 - 3x) = 9 * 2^(2x) - 9.

Step 6: Divide both sides by 4. x^2 - 3x = (9 * 2^(2x) - 9) / 4.

Step 7: Now, to solve for x, you can use numerical methods or graphical methods. There is no simple algebraic way to solve this equation for x, so you may use a graphing calculator or numerical approximation methods like the Newton-Raphson method to find approximate solutions for x.

Please note that the equation might have multiple solutions, and finding exact solutions could be complex depending on the context of the equation.