Question

Вычислить x-y/2
${x}^{3} - {y}^{3} = 3 {x}^{2} y + 5 \\ xy {}^{2} = 1$

Answer 1

x³ -  y³ = 3x²y + 5

xy² = 1

второе умножаем на 3 и складываем с первым

x³ - 3x²y + 3xy² - y³ = 8

(x - y)³ = 2³

x - y = 2

y = x -2

x(x  - 2)² = 1

x³ - 4x² + 4x - 1 = 0

(x - 1)(x² + x + 1) - 4x(x -1) = 0

(x-1)(x² -3x + 1) = 0

x₁ = 1

D=9 - 4 = 5

x₂₃ = (3 +- √5)/2

y = x - 2

y₁ = -1

y₂₃ = 2 - (3+-√5)/2 = (1 -+ √5)/2

(x-y)/2 = 1