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asem2012
@asem2012
August 2022
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Решите Пожалуйста 11-13 номер
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sedinalana
Verified answer
11
а)x²-2x-15≥0
x1+x2=2 U x1*x2=-15⇒x1=-3 U x2=5
x∈(-∞;-3] U [5;∞)
б)x²+6x-18<0
D=36+72=108
x1=(-6-6√3)/2=-3-3√3 U x2=-3+3√3
x∈(-3-3√3;-3+3√3)
в)5x²+4x-9≤0
D=16+180=196
x1=(-4-14)/10=-1,8 U x2=(-4+14)/10=1
x∈[-1,8;1]
г)3y²-7y-10>0
D=49+120=169
y1=(7-13)/6=-1 U y2=(7+13)/6=10/3
y∈(-∞;-1) U (10/3;∞)
12
а)(x+5)(x-3)≤0
x=-5 x=3
x∈[-5;3]
б)(x-7)(x+4)≥0
x=7 x=-4
x∈(-∞;-4] U [7;∞)
в)(x+6)(x-9)<0
x=-6 x=9
x∈(-6;9)
г)(x-2)/(x+11)<0
x=2 x=-11
x∈(-11;2)
д)(x-3)/(x+4)≥0
x=3 x=-4
x∈(-∞;-4) U [3;∞)
е)(x+2)/(x+8)≤0
x=-2 x=-8
x∈(-8;-2]
13
а)|2x+3|<9
-9<2x+3<9
-12<2x<6
-6<x<3
x∈(-6;3)
б)|3x-7|>5
3x-7<-5 U 3x-7>5
3x<2 U 3x>12
x<2/3 U x>4
x∈(-∞;2/3) U (4;∞)
в)|5x+2|≥4,4
5x+2≤-4,4 U 5x+2≥4,4
5x≤-6,4 U 5x≥2,4
x≤-1,28 U x≥0,48
x∈(-∞;-1,28] U [0,48;∞)
г)|2x-9|≤3,5
-3,5≤2x-9≤3,5
5,5≤2x≤12,5
2,75≤x≤6,25
x∈[2,75;6,25]
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Answers & Comments
Verified answer
11а)x²-2x-15≥0
x1+x2=2 U x1*x2=-15⇒x1=-3 U x2=5
x∈(-∞;-3] U [5;∞)
б)x²+6x-18<0
D=36+72=108
x1=(-6-6√3)/2=-3-3√3 U x2=-3+3√3
x∈(-3-3√3;-3+3√3)
в)5x²+4x-9≤0
D=16+180=196
x1=(-4-14)/10=-1,8 U x2=(-4+14)/10=1
x∈[-1,8;1]
г)3y²-7y-10>0
D=49+120=169
y1=(7-13)/6=-1 U y2=(7+13)/6=10/3
y∈(-∞;-1) U (10/3;∞)
12
а)(x+5)(x-3)≤0
x=-5 x=3
x∈[-5;3]
б)(x-7)(x+4)≥0
x=7 x=-4
x∈(-∞;-4] U [7;∞)
в)(x+6)(x-9)<0
x=-6 x=9
x∈(-6;9)
г)(x-2)/(x+11)<0
x=2 x=-11
x∈(-11;2)
д)(x-3)/(x+4)≥0
x=3 x=-4
x∈(-∞;-4) U [3;∞)
е)(x+2)/(x+8)≤0
x=-2 x=-8
x∈(-8;-2]
13
а)|2x+3|<9
-9<2x+3<9
-12<2x<6
-6<x<3
x∈(-6;3)
б)|3x-7|>5
3x-7<-5 U 3x-7>5
3x<2 U 3x>12
x<2/3 U x>4
x∈(-∞;2/3) U (4;∞)
в)|5x+2|≥4,4
5x+2≤-4,4 U 5x+2≥4,4
5x≤-6,4 U 5x≥2,4
x≤-1,28 U x≥0,48
x∈(-∞;-1,28] U [0,48;∞)
г)|2x-9|≤3,5
-3,5≤2x-9≤3,5
5,5≤2x≤12,5
2,75≤x≤6,25
x∈[2,75;6,25]