решите уравнение. (2x+3)(3x+1)=11x+30

(2х + 3) * (3х + 1) = 11х + 30;

2х * 3х + 2х * 1 + 3 * 3х + 3 * 1 = 11х + 30;

6х^2 + 2х + 9х + 3 = 11х + 30;

6х^2 + 2х + 9х - 11х + 3 - 30 = 0;

6х^2 + 11х - 11х - 27 = 0;

6х^2 - 27 = 0;

6х^2 = 27;

х^2 = 27 : 6;

х^2 = (9 * 3)/(3 * 2);

х^2 = 9/2;

х = ±√9/2;

х1 = 3/√2;

х2 = -3/√2;

х1 = (3 * √2)/(√2 * √2);

х2 = (-3 * √2)/(√2 * √2);

х1 = 3√2/2;

х2 = -3√2/2.

Ответ: х1 = 3√2/2, х2 = -3√2/2.

Проверка:

(2 * 3√2/2 + 3) * (3 * 3√2/2 + 1) = 11 * 3√2/2 + 30;

(3√2 + 3) * (9√2/2 + 1) = 33√2/2 + 30;

27 * 2/2 + 3√2 + 27√2/2 + 3 - 33√2/2 - 30 = 0;

27 + 3√2 + 13,5√2 + 3 - 16,5√2 - 30 = 0;

30 - 30 + 16,5√2 - 16,5√2 = 0;

0 = 0.