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utseetstse
@utseetstse
June 2022
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Алгебра 11 класс решите неравенство
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KuOV
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Область определения:
8x>0
0,125x > 0
0,125x ≠ 1
0,5x > 0
0,5x ≠ 1
x > 0
x ≠ 2
x ≠ 8
Пусть log₂x = t
((t + 3)(t - 1) - (t - 3)) / (t - 3) ≤ 0
(t² + t) / (t - 3) ≤ 0
t·(t + 1) / (t - 3) ≤ 0
t ≤ - 1 или 0 ≤ t ≤ 3
log₂x ≤ - 1 0 ≤ log₂x ≤ 3
0< x ≤ 1/2 1 ≤ x ≤ 8
С учетом области определения:
x∈(0 ; 1/2) ∪ [1 ; 2 ) ∪ (2 ; 8 )
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Answers & Comments
Verified answer
Область определения:8x>0
0,125x > 0
0,125x ≠ 1
0,5x > 0
0,5x ≠ 1
x > 0
x ≠ 2
x ≠ 8
Пусть log₂x = t
((t + 3)(t - 1) - (t - 3)) / (t - 3) ≤ 0
(t² + t) / (t - 3) ≤ 0
t·(t + 1) / (t - 3) ≤ 0
t ≤ - 1 или 0 ≤ t ≤ 3
log₂x ≤ - 1 0 ≤ log₂x ≤ 3
0< x ≤ 1/2 1 ≤ x ≤ 8
С учетом области определения:
x∈(0 ; 1/2) ∪ [1 ; 2 ) ∪ (2 ; 8 )