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rapru
@rapru
August 2022
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1) запишите в виде обыкновенной дроби 0,(57)
2) решите неравенство |x^2 - 6x + 5| больше или равно x + 5
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arsenlevadniy
Verified answer
1)
x=0,(57),
100x=57,(57);
99x=57,
x=57/99.
2)
|x^2-6x+5|≥x+5,
[ x^2-6x+5≤-(x+5),
[ x^2-6x+5≥x+5;
[ x^2-5x+10≤0,
[ x^2-7x≥0;
x^2-5x+10=0,
D=-15<0, a=1>0,
x∈Ф.
x^2-7x=0,
x(x-7)=0,
x_1=0, x_2=7,
x∈(-∞0]U[7;+∞).
x∈ФU(-∞0]U[7;+∞)=(-∞0]U[7;+∞),
x∈(-∞0]U[7;+∞).
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Answers & Comments
Verified answer
1)x=0,(57),
100x=57,(57);
99x=57,
x=57/99.
2)
|x^2-6x+5|≥x+5,
[ x^2-6x+5≤-(x+5),
[ x^2-6x+5≥x+5;
[ x^2-5x+10≤0,
[ x^2-7x≥0;
x^2-5x+10=0,
D=-15<0, a=1>0,
x∈Ф.
x^2-7x=0,
x(x-7)=0,
x_1=0, x_2=7,
x∈(-∞0]U[7;+∞).
x∈ФU(-∞0]U[7;+∞)=(-∞0]U[7;+∞),
x∈(-∞0]U[7;+∞).