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Grafkom
@Grafkom
July 2021
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найти сумму наибольшего целого и наименьшего целого решений неравенств:
[tex] \frac{|x-30|(x^2+9)}{|x-7|-10} \leq 0[/tex]
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sedinalana
Verified answer
X²+9>0 при любом х⇒|x-30|/(|x-7|-10)≤0
1)x<7
(30-x)/(7-x-10)≤0
(x-30)/(x+3)≤0
x=30 x=-3
-3<x<30
x∈(-3;7)
2)7≤x<30
(30-x)/(x-7-10)≤0
(x-30)/(x-17)≥0
x=30 x=17
x<17 U x>30
x∈[7;17)
3)x≥30
(x-30)/(x-17)≤0
x=30 x=17
17<x≤30
x=30
Ответ x∈(-3;17) U {30}
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Answers & Comments
Verified answer
X²+9>0 при любом х⇒|x-30|/(|x-7|-10)≤01)x<7
(30-x)/(7-x-10)≤0
(x-30)/(x+3)≤0
x=30 x=-3
-3<x<30
x∈(-3;7)
2)7≤x<30
(30-x)/(x-7-10)≤0
(x-30)/(x-17)≥0
x=30 x=17
x<17 U x>30
x∈[7;17)
3)x≥30
(x-30)/(x-17)≤0
x=30 x=17
17<x≤30
x=30
Ответ x∈(-3;17) U {30}