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SMO 2016 Junior Round 1 Question 8

SMO · SMO 2016 Junior Round 1

Question 8

Two real numbers $u$ and $v$ satisfy the following equations respectively: $$2015u^2+2016u+1=0;\qquad v^2+2016v+2015=0.$$ If $uv\ne1$, find the value of $\frac uv$.
  1. $-\frac{2016}{2015}$
  2. $\frac1{2015}$
  3. $\frac1{2016}$
  4. $\frac{2016}{2015}$
  5. $1$