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Rauau1999
@Rauau1999
July 2022
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Решить относительно x уравнение
Sqrt(x+1)*sqrt(x-2)=a
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nKrynka
Решение
Sqrt(x+1)*sqrt(x-2)=a
ОДЗ: x + 1 > 0, x > - 1
x - 2 > 0, x > 2
ОДЗ: x
∈ (2 + ∞)
√[(x + 1)*(x - 2)] = a
{√[(x + 1)*(x - 2}² = a²
x² - x - 2 = a²
x² - x - (2 + a²) = 0
D = 1 + 4*1*(2 + a²) = 1 + 8 + 4a² = 9 + 4a²
x₁ = [1 - √(9 + 4a²)] / 2 не принадлежит ОДЗ: x∈ (2 + ∞)
x₂ = [1 + √(9 + 4a²)] / 2 = (1/2)*[√(9 + 4a²) + 1] принадлежит ОДЗ: x∈ (2 + ∞)
Ответ: x = (1/2)*[√(9 + 4a²) + 1]
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Answers & Comments
Sqrt(x+1)*sqrt(x-2)=a
ОДЗ: x + 1 > 0, x > - 1
x - 2 > 0, x > 2
ОДЗ: x∈ (2 + ∞)
√[(x + 1)*(x - 2)] = a
{√[(x + 1)*(x - 2}² = a²
x² - x - 2 = a²
x² - x - (2 + a²) = 0
D = 1 + 4*1*(2 + a²) = 1 + 8 + 4a² = 9 + 4a²
x₁ = [1 - √(9 + 4a²)] / 2 не принадлежит ОДЗ: x∈ (2 + ∞)
x₂ = [1 + √(9 + 4a²)] / 2 = (1/2)*[√(9 + 4a²) + 1] принадлежит ОДЗ: x∈ (2 + ∞)
Ответ: x = (1/2)*[√(9 + 4a²) + 1]