Find two positive numbers whose sum is $14$ and product is $48$.

Find two positive numbers whose sum is $14$ and product is $48$.
  1. $6$ and $8$
  2. $4$ and $10$
  3. $2$ and $12$
  4. $7$ and $7$

Solution

Let them be $a,b$. $a+b=14, ab=48$. They are roots of $x^{2}-14x+48=0=(x-6)(x-8)$. So $6$ and $8$.

Asked in: IMO

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