Question

X² + y² = 40xy = 20​

Answer 1

Ответ: см фото.

Объяснение:

Answer 2

The equations you've provided are:

1. x² + y² = 40
2. xy = 20

To work with these equations, you can use various methods, such as substitution or elimination. Let's solve them using the substitution method:

From equation (2), we can express one variable in terms of the other. Let's solve for y:

xy = 20

y = 20/x

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

x² + (20/x)² = 40

Now, simplify the equation:

x² + 400/x² = 40

Multiply both sides of the equation by x² to get rid of the fraction:

x^4 + 400 = 40x²

Rearrange the equation:

x^4 - 40x² + 400 = 0

This is a quadratic equation in terms of x². Let's make a substitution to simplify it further. Let z = x²:

z² - 40z + 400 = 0

Now, you can solve this quadratic equation for z:

(z - 20)(z - 20) = 0

(z - 20)² = 0

Now, take the square root of both sides:

z - 20 = 0

z = 20

Now that we've found the value of z, which is x²:

x² = 20

Take the square root of both sides to find the possible values of x:

x = ±√20

x = ±2√5

Now that you have the values of x, you can find the corresponding values of y using equation (2):

xy = 20

For x = 2√5:

y = 20 / (2√5) = 10 / √5 = 2√5

For x = -2√5:

y = 20 / (-2√5) = -10 / √5 = -2√5

So, the solutions to the system of equations are:

1. x = 2√5, y = 2√5
2. x = -2√5, y = -2√5