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stnastja
@stnastja
August 2022
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Решите пожалуйста 99 а)
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snow99
X² - 2xy + y² = 4
x² + xy = 4
(x - y)² = 4
x² + xy = 4
1) x - y = 2
x² + xy = 4
y = x - 2
x² + x(x - 2) = 4
y = x - 2
x² + x² - 2x - 4 = 0
y = x - 2
2x² - 2x - 4 = 0
y = x - 2
x² - x - 2 = 0
x₁ = 2, y₁ = 0
x₂ = -1, y₂ = -3
2) x - y = -2
x² + xy = 4
y = x + 2
x² + x(x + 2) = 4
y = x + 2
x² + x² + 2x - 4 = 0
y = x + 2
2x² + 2x - 4 = 0
y = x + 2
x² + x - 2 = 0
x₃ = -2, y₃ = 0
x₄ = 1, y₄ = 3
Ответ: (2; 0), (-2; 0), (-1; -3), (1, 3)
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Answers & Comments
x² + xy = 4
(x - y)² = 4
x² + xy = 4
1) x - y = 2
x² + xy = 4
y = x - 2
x² + x(x - 2) = 4
y = x - 2
x² + x² - 2x - 4 = 0
y = x - 2
2x² - 2x - 4 = 0
y = x - 2
x² - x - 2 = 0
x₁ = 2, y₁ = 0
x₂ = -1, y₂ = -3
2) x - y = -2
x² + xy = 4
y = x + 2
x² + x(x + 2) = 4
y = x + 2
x² + x² + 2x - 4 = 0
y = x + 2
2x² + 2x - 4 = 0
y = x + 2
x² + x - 2 = 0
x₃ = -2, y₃ = 0
x₄ = 1, y₄ = 3
Ответ: (2; 0), (-2; 0), (-1; -3), (1, 3)