To find the value of X^2 / Y^2, we need to simplify the given equation and then substitute the values of X and Y.
Given: X + 2Y = 2X + Y
Let`s simplify the equation:
X + 2Y = 2X + Y
X - 2X = Y - 2Y
-X = -Y
Now, let`s square both sides of the equation:
(-X)^2 = (-Y)^2
X^2 = Y^2
Since X^2 is equal to Y^2, we can conclude that X^2 / Y^2 is equal to:
X^2 / Y^2 = Y^2 / Y^2 (substituting X^2 = Y^2)
X^2 / Y^2 = 1
Therefore, X^2 / Y^2 is equal to 1.