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zzzPhenomenalOnezzz
@zzzPhenomenalOnezzz
August 2022
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При каких значениях параметра a, отношение корней уравнения ax^2-(a+3)x+3=0 равно 3/2?
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Verified answer
D=(a+3)²-12a=a²-6a+9=(a-3)²
x₁ = ((a+3) - (a-3)) / (2a) = 6 / (2a) = 3 / a
x₂ = ((a+3) + (a-3)) / (2a) = 2a / (2a) = 1
или (3/a) : 1 = 3/2
a = 2
или 1 : (3/a) = 3/2
a/3 = 3/2
a = 9/2 = 4.5
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Answers & Comments
Verified answer
D=(a+3)²-12a=a²-6a+9=(a-3)²x₁ = ((a+3) - (a-3)) / (2a) = 6 / (2a) = 3 / a
x₂ = ((a+3) + (a-3)) / (2a) = 2a / (2a) = 1
или (3/a) : 1 = 3/2
a = 2
или 1 : (3/a) = 3/2
a/3 = 3/2
a = 9/2 = 4.5