math

If a and b are integers such that a - b = 10, find the minimum value of a*b.

Hello Guest!!

$a-b=10\\ a=10+b\\ ab=10b+b^2\\ \frac{d(ab)}{db}=10+2b=0\\ b=-5\\ a=5\\ \color{blue}ab_{min}=-25$

  !

$a-b=10$

$b=a-10$

and using the rule that a*b is always greater if a and b are closest to each other

$a=5$

so $5*-5=-25$

just like asinus said!