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alla3
@alla3
July 2022
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Решить неравенство:
log2(x^2 - 3x + 2) ≤ log2(x-2) + 1
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nelle987
Verified answer
Log2(x^2 - 3x + 2) <= log2(x - 2) + 1
log2(x^2 - 3x + 2) <= log2(2x - 4)
0 < x^2 - 3x + 2 <= 2x - 4
Первое неравенство:
x^2 - 3x + 2 > 0
(x - 1)(x - 2) > 0
x ∈ (-∞, 1) ∪ (2, +∞)
Второе неравенство:
x^2 - 3x + 2 <= 2x - 4
x^2 - 5x + 6 <= 0
(x - 2)(x - 3) <= 0
x ∈ [2, 3]
Пересекаем ответы и получаем итоговый результат.
x ∈ (2, 3].
Ответ. x ∈ (2, 3].
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Answers & Comments
Verified answer
Log2(x^2 - 3x + 2) <= log2(x - 2) + 1log2(x^2 - 3x + 2) <= log2(2x - 4)
0 < x^2 - 3x + 2 <= 2x - 4
Первое неравенство:
x^2 - 3x + 2 > 0
(x - 1)(x - 2) > 0
x ∈ (-∞, 1) ∪ (2, +∞)
Второе неравенство:
x^2 - 3x + 2 <= 2x - 4
x^2 - 5x + 6 <= 0
(x - 2)(x - 3) <= 0
x ∈ [2, 3]
Пересекаем ответы и получаем итоговый результат.
x ∈ (2, 3].
Ответ. x ∈ (2, 3].