Решите уравнения:a)25=26x-x2;б)3x2=10-29x;в)y2=4y+96;г)3p2+3=10p;д)x2-20x=20x+100;е)25x2-13x=10x2-7;

1) 25 = 26х - х^2.

х^2 - 26х + 25 = 0.

Найдем дискриминант по формуле:

D = b^2 - 4ac = 676 - 4 * 25 = 676 -100 = 576.

x1 = (-b + D)/2a = (26 + 24)/2 = 50/2 = 25.

x2 = (-b - D)/2a = (26 - 24)/2 = 2/2 = 1.

2) 3x^2 = 10 - 29x;

3x^2 + 29x - 10 = 0.

D = 841 + 4 * 3 * 10 = 961.

x1 = (-29 + 31)/6 = 2/6 = 1/3.

x2 = (-29 - 31)/6 = -60/6 = -10.

3) y^2 = 4y + 96;

y^2 - 4y - 96 = 0.

D = 16 + 4 * 96 = 400.

x1 = (4 + 20)/2 = 24/2 = 12.

x2 = (4 - 20)/2 = -16/2 = -8.

4) 3p^2 + 3 = 10p;

3p^2 - 10p + 3 = 0.

D = 100 - 4 * 3 * 3 = 64.

x1 = (10 + 8)/6 = 18/6 = 3.

x2 = (10 - 8)/6 = 2/6 = 1/3.

5) x^2 - 20x = 20x + 100.

x^2 - 20x - 20x - 100 = 0;

x^2 - 40x - 100 = 0.

D = 1600 + 4 * 100 = 2000.

x1 = (40 + 205)/2 = 20 + 105.

x2 = (40 - 205)/2 = 20 - 105.

6) 25x^2 - 13x = 10x^2 - 7;

25x^2 - 10x^2 - 13x + 7 = 0;

15x^2 - 13x + 7 = 0.

D = 169 - 4 * 15 * 7 = -251.

D lt; 0, уравнение не имеет реальных корней.