Question

(2x+3)²-(2x-1)(2x+1)=34​

Answer 1

Ответ:

$(2x + 3) {}^{2} - (2x - 1)(2x + 1) = 34 \\ 4x {}^{2} + 12x + 9 - 4x {}^{2} + 1 = 34 \\ 12x = 34 - 9 - 1 \\ 12x = 24 \\ x = 24 \div 12 \\ x = 2$

Answer 2

To solve the equation (2x+3)² - (2x-1)(2x+1) = 34, follow these steps:

1. Expand the expressions on both sides of the equation:

   (2x+3)² - (2x-1)(2x+1) = 34

   Expand the left side: (2x+3)(2x+3) - (2x-1)(2x+1) = 34

   Using the distributive property (FOIL): (4x² + 12x + 9) - (4x² - 1) = 34

2. Now, simplify the equation by removing parentheses and combining like terms:

   4x² + 12x + 9 - 4x² + 1 = 34

   Note that the 4x² terms cancel out:

   12x + 9 + 1 = 34

3. Combine like terms:

   12x + 10 = 34

4. Subtract 10 from both sides of the equation:

   12x = 34 - 10

   12x = 24

5. Finally, divide both sides by 12 to isolate x:

   x = 24 / 12

   x = 2

So, the solution to the equation is x = 2.