Question

(2х+3)^2+11=12(2х^2+3) решения

Answer 1

(2x + 3)² + 11 = 12(2x² + 3)

4x² + 12x + 9 + 11 = 24x² + 36

24x² - 4x² - 12x + 36 - 20 = 0

20x² - 12x + 16 = 0

5x² - 3x + 4 = 0

D = (- 3)² - 4 * 5 * 4 = 9 - 80  = - 71 < 0

Ответ : корней нет

Answer 2

To solve the equation (2x + 3)^2 + 11 = 12(2x^2 + 3), we can follow these steps:

Step 1: Expand the squared term on the left side of the equation.

(2x + 3)^2 + 11 = 12(2x^2 + 3) (4x^2 + 12x + 9) + 11 = 12(2x^2 + 3) 4x^2 + 12x + 20 = 24x^2 + 36

Step 2: Move all terms to one side of the equation to set it equal to zero.

0 = 24x^2 - 4x^2 + 12x - 12x + 36 - 20 0 = 20x^2 - 24

Step 3: Simplify the equation further.

0 = 5x^2 - 6

Step 4: Set the equation equal to zero.

5x^2 - 6 = 0

Step 5: Solve the quadratic equation by factoring or using the quadratic formula.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 5, b = 0, and c = -6.

x = (-(0) ± √((0)^2 - 4(5)(-6))) / (2(5)) x = ± √(0 + 120) / 10 x = ± √(120) / 10 x = ± √(12 * 10) / 10 x = ± (√12 * √10) / 10 x = ± (√4 * √3 * √10) / 10 x = ± (2√3 * √10) / 10 x = ± (2√30) / 10 x = ± (√30) / 5

Therefore, the solutions to the equation are: x = (√30) / 5 x = - (√30) / 5