Решите уравнения (2x-3) ^2=11x-19 (x+1) ^2=7918-2x (x+2) ^2=3131-2x

Решим уравнение:

1) (2 х - 3) ^2 = 3131 - 2x;

4 х^2 - 12 х + 9 = 3131 - 2x;

4 х^2 - 12 х + 9 - 3131 + 2x = 0;

4x^2 - 10x - 3122 = 0;

D = b^2 - 4ac = 100 + 49952 = 50052;

x = (-b ± √D) / 2a = (10 ± 2√12513) / 8 = (5 ± √12513) / 4.

2) 11x - 19 * (x + 1) ^2 = 3131 - 2x;

11x - 19x^2 - 38x - 19 = 3131 - 2x;

-17x^2 - 27x - 3150 = 0;

D = 729 + 214200 = 214929;

x = (27 ± 3√23881) / (-34).

3) 7918 - 2 * (x + 2) ^2 = 3131 - 2x;

7918 - 2 * (x^2 + 4x + 4) = 3131 - 2x;

7918 - 2x^2 + 8x - 8 - 3131 + 2x = 0;

-2x^2 + 10x + 4779 = 0;

D = 100 + 38232 = 38332;

x = (-10 ± 2√9583) / (-4) = (-5 ± √9583) / (-2).