Question

Найдите сумму корней уравнения 3(x+4)^2+5|x+4|-2=0

Answer 1

3(x+4)²+5|x+4|-2=0
x+4=0
x=-4
1) x≤-4   3(x+4)²-5(x+4)-2=0        t=x+4
             3t²-5t-2=0
             D=49=7²
             t1=2                           t2= -1/3
             x+4=2                        x+4=-1/3
             x=-2∉(-∞;-4]              x=-4 1/3∈(-∞;-4]  

2) x>-4  3(x+4)²+5(x+4)-2=0      t=x+4
             3t²+5t-2=0
             D=49=7²
             t3=1/3                             t4=-2
             x+4= 1/3                         x+4=-2
             x=-3 2/3∈(4;+∞)            x=-6∉(4;+∞)

S=(-4 1/3)+( -3 2/3) = -8
Ответ: -8