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Чонин88
@Чонин88
August 2022
2
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решить уравнения:
а) |4х²+5х-9|=75
б) |5х²-3х-7|=|х²-2х-7|
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Kixcertborn2
Verified answer
|4х²+5х-9|=75
4x^2+5x-9=75 4x^2+5x-9=-75
4x^2+5x-9-75=0 4x^2+5x-9+75=0
4x^2+5x-84=0 4x^2+5x+66=0
D=25+1344=1369=37^2 D=25-1056=-1031===>>решений нет
x=(-5
±37)/8 x∉R
x₁=4
x
₂=-(21/4)
==========================================================
|5х²-3х-7|=|х²-2х-7|
5x^2-3x-7=x^2-2x-7 5x^2-3x-7=-(x^2-2x-7)
5x^2-3x=x^2-2x
5x^2-3x-7=-x^2+2x+7
5x^2-3x-x^2+2x=0 5x^2-3x-7+x^2-2x-7=0
x*(5x-3-x+2)=0 6x^2-5x-14=0
x*(4x-1)=0 D=(-5)^2-4*6*(-14)=25+336=361=19^2
x=0 x
₁=0 x=(5±19)/12
4x-1=0 x
₂=1/4 x₃=2 x₄=-(7/6)
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Answers & Comments
Verified answer
|4х²+5х-9|=754x^2+5x-9=75 4x^2+5x-9=-75
4x^2+5x-9-75=0 4x^2+5x-9+75=0
4x^2+5x-84=0 4x^2+5x+66=0
D=25+1344=1369=37^2 D=25-1056=-1031===>>решений нет
x=(-5±37)/8 x∉R
x₁=4
x₂=-(21/4)
==========================================================
|5х²-3х-7|=|х²-2х-7|
5x^2-3x-7=x^2-2x-7 5x^2-3x-7=-(x^2-2x-7)
5x^2-3x=x^2-2x 5x^2-3x-7=-x^2+2x+7
5x^2-3x-x^2+2x=0 5x^2-3x-7+x^2-2x-7=0
x*(5x-3-x+2)=0 6x^2-5x-14=0
x*(4x-1)=0 D=(-5)^2-4*6*(-14)=25+336=361=19^2
x=0 x₁=0 x=(5±19)/12
4x-1=0 x₂=1/4 x₃=2 x₄=-(7/6)