**Quote:**

therefore *x*² + *y*² =(-4)

The result you got is impossible, because the sum of two squares must be a non-negative number. Therefore there must be a mistake in your reasoning.

Here it is:

**Quote:**

*x*² + *y*² = *x*² + 2*xy* + *y*²

so: *x*² + *y*² = -2*xy*

The first equality is true only if one of the variables is 0 because it can be simplified into 0 = 2

*xy*. Probably, you confused it with (

*x* +

*y*)² =

*x*² + 2

*xy* +

*y*², which is true for any values.

The second equality does NOT come from the first one. It is the same as

*x*² + 2

*xy* +

*y*² = 0, which is (

*x* +

*y*)² = 0.

That is NOT implied by anything in the question statement.