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ludaкоз
@ludaкоз
July 2022
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mod(x**2-5x+4)<=mod(x**2-4)
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sedinalana
Verified answer
|x²-5x+4|≤|x²-4|
|(x-1)(x-4)|≤|(x-2)(x+2)|
1)x<-2
x²-5x+4≤x²-4
-5x≤-8
x≥1,6
нет решения
2)-2≤x<1
x²-5x+4≤-x²+4
2x²-5x≤0
2x(x-2,5)≤0
x=0 x=2,5
0≤x<2,5 U -2≤x<1⇒0≤x<1
3)1≤x<2
-x²+5x-4≤-x²+4
5x≤8
x≤1,6
1≤x≤1,6
4)2≤x<4
-x²+5x-4≤x²-4
-2x²+5x≤0
2x²-5x≥0
2x(x-2,5)≥0
x=0 x=2,5
x≤0 U x≥2,5 U 2≤x<4⇒2,5≤x<4
5)x≥4
x²-5x+4≤x²-4
-5x≤-8
x≥1,6 U x≥4⇒x≥4
x∈[0;1,6] U [2,5;∞)
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Answers & Comments
Verified answer
|x²-5x+4|≤|x²-4||(x-1)(x-4)|≤|(x-2)(x+2)|
1)x<-2
x²-5x+4≤x²-4
-5x≤-8
x≥1,6
нет решения
2)-2≤x<1
x²-5x+4≤-x²+4
2x²-5x≤0
2x(x-2,5)≤0
x=0 x=2,5
0≤x<2,5 U -2≤x<1⇒0≤x<1
3)1≤x<2
-x²+5x-4≤-x²+4
5x≤8
x≤1,6
1≤x≤1,6
4)2≤x<4
-x²+5x-4≤x²-4
-2x²+5x≤0
2x²-5x≥0
2x(x-2,5)≥0
x=0 x=2,5
x≤0 U x≥2,5 U 2≤x<4⇒2,5≤x<4
5)x≥4
x²-5x+4≤x²-4
-5x≤-8
x≥1,6 U x≥4⇒x≥4
x∈[0;1,6] U [2,5;∞)