If x and y are real numbers such that x^2+(x-2y-1)^2=-4y(x+y), then the value x-2y is

Options

1. 0
2. 1
3. 2
4. -1

Correct Answer

1

Explanation

Expanding the equation: x^2+x^2-4xy-2x+4y^2+4y+1=-4xy-4y^2. Simplifying: 2x^2-2x+8y^2+4y+1=0. This can be rewritten as (x-2y-1)^2+(x)^2+4y^2+4y+1=0, which simplifies to show x-2y=1.

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