(x+3)(x+1)(x+5)(x+7)=9 найти корни

Найдем корни уравнения.

(x + 3) * (x + 1) * (x + 5) * (x + 7) = 9; 

(x + 3) * (x + 5) * (x + 7) * (x + 1) = 9;  

(x^2 + 5 * x + 3 * x + 5 * 3) * (x^2 + 1 * x + 7 * x + 7 * 1) = 9; 

(x^2 + 5 * x + 3 * x + 15) * (x^2 + x + 7 * x + 7) = 9; 

(x^2 + 8 * x + 15) * (x^2 + 8 * x + 7) = 9; 

Пусть x^2 + 8 * x = a, тогда: 

(a + 15) * (a + 7) = 9; 

a^2 + 7 * a + 15 * a + 15 * 7 - 9 = 0; 

a^2 + 22 * a + 105 - 9 = 0; 

a^2 + 22 * a + 96 = 0; 

D = 22^2 - 4 * 1 * 96 = 484 - 4 * 96 = 484 - 384 = 100; 

a1 = (-22 + 10)/2 = -12/2 = -6; 

a2 = (-22 - 10)/2 = -32/2 = -16; 

Получаем: 

1) x^2 + 8 * x = -6; 

x^2 + 8 * x + 6 = 0; 

x1 = -4 - √10; 

x2 = -4 + √10;  

2) x^2 + 8 * x = -16; 

x^2 + 8 * x + 16 = 0; 

x = -4.