Discussion
If x+2y = 2x+y, then the value of \(\frac{x^{2}}{y^{2}}\) is
Answer: B
The value of \(\frac{x^2}{y^2}\) is 1.
Collect the terms of the given equation:
\[ \begin{aligned} x + 2y &= 2x + y \\ 2y - y &= 2x - x \\ y &= x \end{aligned} \]
Since x and y are equal, \(\frac{x^2}{y^2} = 1\) (taking \(y \neq 0\), so that the fraction is defined). The value 0 would need x = 0, and 2 or 4 would need x to be a multiple of y, which the equation does not allow.
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