Question

Решите пример (x^+3x+4)(x^+3x+9)=266

Answer 1

(x^2 + 3x + 4) ( x^2  +3x + 9) = 266
Пусть x^2 + 3x + 4 = t  , тогда
t ( t  + 5) - 266 = 0 
t^2 + 5t - 266 = 0 
D = 25 + 4*266 = 1089 = 33^2
t₁ = ( - 5 +33)/2 = 14
t₂ =  ( - 5 - 33)/2 = - 19

#1
x^2 + 3x + 4 = 14
x^2 + 3x - 10 = 0 
D = 9 + 40 = 49
x₁ = ( - 3 + 7)/2 = 2;
x₂ = ( -  3 - 7)/2 = - 5

#2
x^2  +3x + 4 = - 19
x^2 + 3x + 23 = 0
D = 9 - 4*23 = - 83 < 0 

Ответ:
- 5; 2