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If-15-10-1-3-a-lt-20-find-a-R-

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Question Number 112280 by bemath last updated on 07/Sep/20
If 15 ≤ ∣10−(1/3)a∣ < 20 find a ∈ R
If15⩽∣10−13a∣<20finda∈R
Answered by john santu last updated on 07/Sep/20
⇒ ∣10−(1/3)a∣ ≥15 ∧ ∣10−(1/3)a∣ < 20 (1) ∣10−(1/3)a∣ ≥ 15 10−(1/3)a ≤ −15 ∪ 10−(1/3)a ≥15 −(1/3)a ≤ −25 ∪ −(1/3)a ≥ 5 a ≥ 75 ∪ a ≤−15 (2) ∣10−(1/3)a∣ < 20 −20 < 10−(1/3)a < 20 −30 < −(1/3)a < 10 −30<a<90 solution (1)∩(2) −30< a≤ −15 ∪ 75 ≤ a < 90
⇒∣10−13a∣⩾15∧∣10−13a∣<20(1)∣10−13a∣⩾1510−13a⩽−15∪10−13a⩾15−13a⩽−25∪−13a⩾5a⩾75∪a⩽−15(2)∣10−13a∣<20−20<10−13a<20−30<−13a<10−30<a<90solution(1)∩(2)−30<a⩽−15∪75⩽a<90
Answered by ajfour last updated on 07/Sep/20
(a−30)^2 ≥45^2 & (a−30)^2 <60^2 ⇒ 45≤ a−30 < 60 or −60 < a−30 ≤ −45
(a−30)2⩾452&(a−30)2<602⇒45⩽a−30<60or−60<a−30⩽−45
Commented by bemath last updated on 07/Sep/20
(a−30)^2 ≥ 45^2
(a−30)2⩾452

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