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DanielCarroll
@DanielCarroll
July 2022
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Найдите сумму корней уравнения 3(x+4)^2+5|x+4|-2=0
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Verified answer
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
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Answers & Comments
Verified answer
3(x+4)²+5|x+4|-2=0x+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