Question

( 2x – 3y)2 + (3x - y)(y + 3x) - 4x + 12xy= 5x²- y​

Answer 1

Ответ две в прикрепленном фото, первое относительно х, второе относительно у

Answer 2

Let's simplify the given expression step by step:

(2x - 3y)^2 + (3x - y)(y + 3x) - 4x + 12xy = 5x^2 - y

First, let's expand the squares:

(4x^2 - 12xy + 9y^2) + (3xy + 9x^2 - y^2 - 3xy) - 4x + 12xy = 5x^2 - y

Now, combine like terms:

4x^2 - 12xy + 9y^2 + 3xy + 9x^2 - y^2 - 3xy - 4x + 12xy = 5x^2 - y

Now, let's simplify further:

(4x^2 + 9x^2) + (-12xy + 3xy - 3xy + 12xy) + 9y^2 - y^2 - 4x = 5x^2 - y

Combine like terms again:

13x^2 + 0 + 8y^2 - 4x = 5x^2 - y

Now, let's move all the terms to one side of the equation:

13x^2 - 5x^2 + 8y^2 + 4x = -y

Simplify the x^2 terms and x terms:

8x^2 + 8y^2 + 4x = -y

Now, let's rearrange the equation to match the form of a standard equation of a conic section:

8x^2 + 4x + 8y^2 + y = 0

So, the simplified form of the given expression is:

8x^2 + 4x + 8y^2 + y = 0

This equation represents a conic section, which is an ellipse.