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SMO 2011 Senior Round 1 Question 4

SMO · SMO 2011 Senior Round 1

Question 4

Suppose real numbers $x,y$ satisfy $\frac1x-\frac1{2y}=\frac1{2x+y}$. Find $\frac{y^2}{x^2}+\frac{x^2}{y^2}$.
  1. $\frac23$
  2. $\frac92$
  3. $\frac94$
  4. $\frac49$
  5. $\frac29$