Question

X2 + 7 xy + y2 = 35,xy = 2 найдите |X+Y|​

Answer 1

Ответ:

5.

Пошаговое объяснение:

{х² + 7ху + у² = 35,

{ху = 2;

{х² + 2ху + у² + 5ху = 35,

{ху = 2;

{(х + у)² + 5ху = 35,

{ху = 2;

{(х + у)² + 5•2 = 35,

{ху = 2;

Из первого уравнения системы получим, что

(х + у)² + 10 = 35

(х + у)² = 35 - 10

(х + у)² = 25

l x + yl = √25

l x + yl = 5

Ответ: 5.

Answer 2

Given the equations:

1. x^2 + 7xy + y^2 = 35
2. xy = 2

Let's solve these equations to find the values of x and y. First, we can solve equation (2) for y:

xy = 2

Divide both sides by x:

y = 2/x

Now, substitute this expression for y into equation (1):

x^2 + 7x(2/x) + (2/x)^2 = 35

Simplify:

x^2 + 14 + 4/x^2 = 35

Multiply through by x^2 to get rid of the fraction:

x^4 + 14x^2 + 4 - 35x^2 = 0

Combine like terms:

x^4 - 21x^2 + 4 = 0

Now, let's make a substitution to simplify this equation. Let u = x^2:

u^2 - 21u + 4 = 0

Now, we can use the quadratic formula to solve for u:

u = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -21, and c = 4. Plugging these values into the quadratic formula:

u = (-(-21) ± √((-21)^2 - 4(1)(4))) / (2(1))

u = (21 ± √(441 - 16)) / 2

u = (21 ± √425) / 2

Now, we have two possible values for u:

1. u₁ = (21 + √425) / 2
2. u₂ = (21 - √425) / 2

Now, we can find the corresponding values of x:

1. For u₁: x₁^2 = (21 + √425) / 2 x₁ = ±√((21 + √425) / 2)

2. For u₂: x₂^2 = (21 - √425) / 2 x₂ = ±√((21 - √425) / 2)

Now that we have multiple potential values for x, let's calculate the corresponding values for y using equation (2):

1. For x₁: y₁ = 2 / x₁

2. For x₂: y₂ = 2 / x₂

Now, we can find the possible pairs of (x, y) and calculate |X + Y| for each pair. Finally, we'll take the absolute value of the sum of the pairs to find |X + Y|.

Please note that we have multiple solutions for (x, y) due to the quadratic equation, so we'll have multiple |X + Y| values depending on which (x, y) pairs you choose.