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1CheshireCat1
@1CheshireCat1
July 2022
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Сканави номер 6.144 помогите
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Эксперт5
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(x²+2x)²-(x+1)²=55
(x²+2x)²-(x²+2x+1)=55
(x²+2x)²-[(x²+2x)+1]=55
Замена: y=x²+2x
y²-(y+1)=55
y²-y-1-55=0
y²-y-56=0
По теореме Виета: y₁*y₂=-56 и y₁+y₂=1 => y₁=-7; y₂=8
Обратная замена:
x²+2x=-7 x²+2x=8
x²+2x+7=0 x²+2x-8=0
D=2²-4*1*7=4-28=-24<0 x₁*x₂=-8 и x₁+x₂=-2 =>
Решений нет => x₁=2 и x₂=-4
Ответ: -4 и 2
1 votes
Thanks 2
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Answers & Comments
Verified answer
(x²+2x)²-(x+1)²=55(x²+2x)²-(x²+2x+1)=55
(x²+2x)²-[(x²+2x)+1]=55
Замена: y=x²+2x
y²-(y+1)=55
y²-y-1-55=0
y²-y-56=0
По теореме Виета: y₁*y₂=-56 и y₁+y₂=1 => y₁=-7; y₂=8
Обратная замена:
x²+2x=-7 x²+2x=8
x²+2x+7=0 x²+2x-8=0
D=2²-4*1*7=4-28=-24<0 x₁*x₂=-8 и x₁+x₂=-2 =>
Решений нет => x₁=2 и x₂=-4
Ответ: -4 и 2