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teslam1
@teslam1
July 2022
1
11
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если можно
сам ход решения
мозгов нет, сама не разберусь
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KuOV
Verified answer
X² + 4x + 9 = ax² + 5ax + 9a
x² + 4x + 9 - ax² - 5ax - 9a = 0
(1 - a)x² + (4 - 5a)x + 9(1 - a) = 0
Уравнение имеет корни, если дискриминант ≥ 0
D = (4 - 5a)² - 4· 9(1 - a)² = 16 - 40a + 25a² - 36(1 - 2a + a²) =
= 16 - 40a + 25a² - 36 +72a - 36a² = - 11a² + 32a - 20
- 11a² + 32a - 20 ≥ 0
11a² - 32a + 20 ≤ 0
D/4 = 16² - 11·20 = 256 - 220 = 36
a = (16 - 6)/11 = 10/11 или a = (16 + 6)/11 = 2
a ∈ [10/11 ; 2]
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Answers & Comments
Verified answer
X² + 4x + 9 = ax² + 5ax + 9ax² + 4x + 9 - ax² - 5ax - 9a = 0
(1 - a)x² + (4 - 5a)x + 9(1 - a) = 0
Уравнение имеет корни, если дискриминант ≥ 0
D = (4 - 5a)² - 4· 9(1 - a)² = 16 - 40a + 25a² - 36(1 - 2a + a²) =
= 16 - 40a + 25a² - 36 +72a - 36a² = - 11a² + 32a - 20
- 11a² + 32a - 20 ≥ 0
11a² - 32a + 20 ≤ 0
D/4 = 16² - 11·20 = 256 - 220 = 36
a = (16 - 6)/11 = 10/11 или a = (16 + 6)/11 = 2
a ∈ [10/11 ; 2]