Question

X2 - 2016x= y2 - 2016y

Answer 1

x²-2016*x=y²-2016*y

x²-y²-2016*x+2016*y=0

(x-y)*(x+y)-2016*(x-y)=0

(x-y)*(x+y-2016)=0

x=y

x+y-2016=0    x+y=2016       2x=2016  |÷2     x=1008     ⇒

Ответ: x=y=1008.

Answer 2

To analyze the given equation $X^2 - 2016X = Y^2 - 2016Y$, let's try to understand its properties. This equation is a second-degree equation (quadratic) with two variables, X and Y.

To further simplify and manipulate the equation, let's move all the terms to one side of the equation:

$X^2 - 2016X - Y^2 + 2016Y = 0$

Now, let's see if we can factor this equation. Notice that the equation can be expressed as the difference of two squares:

$X^2 - 2016X = (X^2 - 2016X) - (Y^2 - 2016Y) = X(X - 2016) - Y(Y - 2016)$

Thus, the equation can be factored as:

$X(X - 2016) - Y(Y - 2016) = 0$

Now, we have a quadratic equation in terms of X and Y. However, it is not possible to find a unique solution for both X and Y with just this equation since we have two variables and only one equation. We need additional information or equations to determine specific values for X and Y.

If you have any more information or another equation related to X and Y, please provide it, and we can try to find a solution for the system of equations.