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NastyaMoore
@NastyaMoore
July 2022
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система уравнений x^2+y^2=8,xy=4
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nKrynka
Решение
x^2+y^2=8,
xy = 4
y = 4/x
x
² + (4/x)² = 8 умножаем на x ≠ 0
x⁴ - 8x² + 16 = 0
x²= t
t² - 8t + 16 = 0
(t - 4)² = 0
t = 4
x² = 4
x₁ = - 2
x₂ = 2
1) x₁ = - 2
y₁ = 4/(-2)
y₁ = - 2
x₂ = 2
y₂ = 4/2
y₂ = 2
Ответ: (- 2; - 2) ; (2; 2)
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Answers & Comments
x^2+y^2=8,
xy = 4
y = 4/x
x² + (4/x)² = 8 умножаем на x ≠ 0
x⁴ - 8x² + 16 = 0
x²= t
t² - 8t + 16 = 0
(t - 4)² = 0
t = 4
x² = 4
x₁ = - 2
x₂ = 2
1) x₁ = - 2
y₁ = 4/(-2)
y₁ = - 2
x₂ = 2
y₂ = 4/2
y₂ = 2
Ответ: (- 2; - 2) ; (2; 2)