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varyaXD
@varyaXD
July 2022
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Помогите пожалуйста! Имеет ли эта система решение?
\left \{ { x^{2}-y ^{2} =3 ;\\ xy=2
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nKrynka
Решение
x² - y² = 3
xy = 2
y = 2/x
x² - 4/x² - 3 = 0
x⁴ - 3x² - 4 = 0
x² = z
z² - 3z - 4 = 0
z₁ = - 1
z₂ = 4
x² = - 1 решений нет
x² = 4
x₁ = - 2
x₂ = 2
x₁ = - 2
y₁ = 2/-2
y₁ = - 1
x₂ = 2
y₂ = 2/2
y₂ = 1
Ответ: (- 2; - 1) ; (2; 1)
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Answers & Comments
x² - y² = 3
xy = 2
y = 2/x
x² - 4/x² - 3 = 0
x⁴ - 3x² - 4 = 0
x² = z
z² - 3z - 4 = 0
z₁ = - 1
z₂ = 4
x² = - 1 решений нет
x² = 4
x₁ = - 2
x₂ = 2
x₁ = - 2
y₁ = 2/-2
y₁ = - 1
x₂ = 2
y₂ = 2/2
y₂ = 1
Ответ: (- 2; - 1) ; (2; 1)