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feanutri
@feanutri
July 2022
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Решите пожалуйста систему неравенств
-13<=4x+3<18
log3 (x^2-7)>=2
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nKrynka
Решение
-13<=4x+3<18
log3 (x^2-7)>=2
ОДЗ: x² - 7 > 0, x² = 7, x₁ = - √7 ; x₂ = √7
x∈( - ∞ ; - √7) (√7 ; + ∞)
1) -13 - 3 ≤ 4x < 18 - 3
- 16 ≤ 4x < 15
- 4 ≤ x < 3,75
2) log₃ (x² - 7) ≥ 2
x² - 7 ≥ 3²
x² ≥ 9 + 7
x² ≥ 16
x₁ = - 4
x₂ = 4
x ∈ ( - ∞ ; - 4) (4 ; + ∞)
Ответ: 4
1 votes
Thanks 2
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Answers & Comments
-13<=4x+3<18
log3 (x^2-7)>=2
ОДЗ: x² - 7 > 0, x² = 7, x₁ = - √7 ; x₂ = √7
x∈( - ∞ ; - √7) (√7 ; + ∞)
1) -13 - 3 ≤ 4x < 18 - 3
- 16 ≤ 4x < 15
- 4 ≤ x < 3,75
2) log₃ (x² - 7) ≥ 2
x² - 7 ≥ 3²
x² ≥ 9 + 7
x² ≥ 16
x₁ = - 4
x₂ = 4
x ∈ ( - ∞ ; - 4) (4 ; + ∞)
Ответ: 4