If $(x + a)(x + b) = x^{2} + 13x + 36$ and $a > b > 0$, find $a - b$.

If $(x + a)(x + b) = x^{2} + 13x + 36$ and $a > b > 0$, find $a - b$.
  1. $5$
  2. $13$
  3. $36$
  4. $1$

Solution

$a + b = 13,\ ab = 36 \Rightarrow a = 9, b = 4$. So $a - b = 5$.

Asked in: IMO

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