If $a^{2} - b^{2} = 60$ and $a + b = 10$, find $a - b$.

If $a^{2} - b^{2} = 60$ and $a + b = 10$, find $a - b$.
  1. $6$
  2. $10$
  3. $5$
  4. $60$

Solution

$a^{2} - b^{2} = (a+b)(a-b) \Rightarrow 60 = 10 \cdot (a-b) \Rightarrow a - b = 6$.

Asked in: IMO

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