Сделаем замену переменной y = x^2 - 5x. Тогда
(y+2)*(y-1) = 28
y^2 - y + 2y - 2 = 28;
y^2 + y - 30 = 0;
D = 1 - 4*(-30) = 1+120 = 121 = 11^2;
y1 = (-1-11)/2 = -12/2 = -6;
y2 = (-1+11)/2 = 10/2 = 5.
1) x^2 - 5x = -6;
x^2 - 5x + 6 = 0;
D = 5^2 - 4*6 = 25 - 24 = 1;
x1 = (5 - 1)/2 = 4/2 = 2;
x2 = (5+1)/2 = 6/2 = 3.
2) x^2 - 5x = 5;
x^2 - 5x - 5 = 0;
D = 5^2 - 4*(-5) = 25 + 20 = 45;
x3 и x4 существуют, т.к. D = 45>0,
их произведение по теореме Виета = -5;
x3*x4 = -5;
x1*x2*x3*x4 = 2*3*(-5) = -30.