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knopka143
@knopka143
July 2022
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Помогите решить уравнение!
(x^2+2x)^2-7(x^2+2x)-8=0
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Эксперт5
Verified answer
(x²+2x)² - 7(x²+2x) - 8 = 0
Замена: y=x²+2x
y² - 7y - 8 = 0
D=(-7)²-4*1*(-8) = 49 + 32 = 81
y₁ = (7+√81)/2 = (7+9)/2 = 16/2 = 8
y₂ = (7-√81)/2 = (7-9)/2 = -2/2 =-1
x²+2x=8 x²+2x=-1
x²+2x-8=0 x²+2x+1=0
D=2²-4*1*8=4-32=-28<0 (x+1)²=0
Решений нет х+1=0
х=-1
Ответ: -1
4 votes
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Answers & Comments
Verified answer
(x²+2x)² - 7(x²+2x) - 8 = 0Замена: y=x²+2x
y² - 7y - 8 = 0
D=(-7)²-4*1*(-8) = 49 + 32 = 81
y₁ = (7+√81)/2 = (7+9)/2 = 16/2 = 8
y₂ = (7-√81)/2 = (7-9)/2 = -2/2 =-1
x²+2x=8 x²+2x=-1
x²+2x-8=0 x²+2x+1=0
D=2²-4*1*8=4-32=-28<0 (x+1)²=0
Решений нет х+1=0
х=-1
Ответ: -1