Предмет: Алгебра, автор: bayanturkmenova18

(xy=2(x+y) Lorry10x+y-27=10y+x​

Ответы

Автор ответа: Morozz89
0

Ответ:

(x, y) = (2 - 2√3, 4 - 2√3) or (2 + 2√3, 4 + 2√3)

Объяснение:

Quadratic Solution for Two Equations

nealglie_41

(xy=2(x+y) Lorry10x+y-27=10y+x

To solve the given equations:

xy = 2(x+y) --------(1)

Lorry10x+y-27=10y+x --------(2)

Let's simplify equation (2) by rearranging the terms:

10x - x + y - 10y = 27

9x - 9y = 27

x - y = 3 --------(3)

Now, we can solve for x and y by substituting equation (3) into equation (1):

y(x-y) = 2(x+y)

xy - y^2 = 2x + 2y

Substituting x - y = 3, we get:

xy - y^2 = 2(x+y)

xy - y^2 = 2(3+y)

xy - y^2 = 6 + 2y

Rearranging, we get a quadratic equation:

y^2 - (2+x)y + 6 = 0

Using the quadratic formula, we get:

y = (2+x) ± √(x^2 - 4x - 8) / 2

For y to be a real number, the discriminant (x^2 - 4x - 8) must be non-negative:

x^2 - 4x - 8 ≥ 0

Solving for x, we get:

x ≤ 2 - 2√3 or x ≥ 2 + 2√3

Substituting these values of x into the quadratic formula, we get corresponding values of y. Thus, the solution to the system of equations is:

(x, y) = (2 - 2√3, 4 - 2√3) or (2 + 2√3, 4 + 2√3)

Автор ответа: shuliarv
0

Ответ:

Объяснение:

даш каронку

Приложения:
Похожие вопросы