If $x^{2} - y^{2} = 36$ and $x - y = 4$, find $x + y$.

If $x^{2} - y^{2} = 36$ and $x - y = 4$, find $x + y$.
  1. $9$
  2. $8$
  3. $6$
  4. $12$

Solution

$x^{2}-y^{2}=(x-y)(x+y)$, so $(x+y) = \dfrac{36}{4}=9$.

Asked in: IMO

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