Решите уравнение (2 х-1) (2 х+1) - 4 (х+5) в квадрате

(2 х - 1) (2 х + 1) - 4 (х + 5) ^2 = 0;

4x^2 + 2x - 2x - 1^2 - 4 (x^2 + 2 * x * 5 + 5^2) = 0;

4x^2 - 1 - 4 (x^2 + 10x + 25) = 0;

4x^2 - 1 - 4x^2 - 40x - 100 = 0;

-1 - 100 - 40x = 0;

-101 - 40x = 0;

-40x = 101;

40x = - 101;

x = - 101 : 40;

x = - 2,525.

Проверка:

(2 * (-2,525) - 1) (2 * (-2,525) + 1) - 4 (-2,525 + 5) ^2 = 0;

(-5,05 - 1) (-5,05 + 1) - 4 * (2,475) ^2 = 0;

(-6,05) * (-4,05) - 4 * 6,125625 = 0;

24,5025 - 24,5025 = 0;

0 = 0.

Ответ: x = - 2,525.