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nribaruk
@nribaruk
August 2022
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Розв'язати нерівність: 9x²- модуль х-3 > 9x-2
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sedinalana
Verified answer
9x²-|x-3|>9x-2
1)x<3
9x²+x-3-9x+2>0
9x²-8x-1>0
D=64+36=100
x1=(8-10)/18=-1/9 U x2=(8+10)/18=1
x<-1/9 U x>1
x∈(-∞;-1/9)
2)x≥3
9x²-x+3-9x+2>0
9x²-10x+5=0
D=100-180=-80
х-любое
x∈[3;∞)
Ответ x∈(-∞;-1/9) U [3;∞)
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Answers & Comments
Verified answer
9x²-|x-3|>9x-21)x<3
9x²+x-3-9x+2>0
9x²-8x-1>0
D=64+36=100
x1=(8-10)/18=-1/9 U x2=(8+10)/18=1
x<-1/9 U x>1
x∈(-∞;-1/9)
2)x≥3
9x²-x+3-9x+2>0
9x²-10x+5=0
D=100-180=-80
х-любое
x∈[3;∞)
Ответ x∈(-∞;-1/9) U [3;∞)