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borz9559
@borz9559
June 2022
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Решить неравенство (3x-2)^2>=3x(x-0,5)
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nKrynka
Решение
(3x-2)^2 ≥ 3x(x-0,5)
9x² - 12x + 4 ≥ 3x² - 1,5x
6x² - 10,5x + 4 ≥ 0
D = (− 10.5)²
− 4*6*4 = 110,25 − 96 = 14,25
x₁
= (
10,5 - √14,25) / (2*6)
x
₁
= (
10,5 - √14,25) /
12
x₂
= (
10,5 + √14,25) / (
2*6)
x
₂
= (
10,5 + √14,25) /
12
x
∈ ( - ∞ ; 10,5 - √14,25) / 12] [10,5 + √14,25) / 12 ; + ∞)
1 votes
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Answers & Comments
(3x-2)^2 ≥ 3x(x-0,5)
9x² - 12x + 4 ≥ 3x² - 1,5x
6x² - 10,5x + 4 ≥ 0
D = (− 10.5)² − 4*6*4 = 110,25 − 96 = 14,25
x₁ = (10,5 - √14,25) / (2*6)
x₁ = (10,5 - √14,25) / 12
x₂ = (10,5 + √14,25) / (2*6)
x₂ = (10,5 + √14,25) / 12
x ∈ ( - ∞ ; 10,5 - √14,25) / 12] [10,5 + √14,25) / 12 ; + ∞)