If a and b are integers such that a - b = 10, find the minimum value of a*b.
+14995 If a and b are integers such that a - b = 10, find the minimum value of a*b.
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\(a-b=10\\ a=10+b\\ ab=10b+b^2\\ \frac{d(ab)}{db}=10+2b=0\\ b=-5\\ a=5\\ \color{blue}ab_{min}=-25\)
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+364 \(a-b=10\)
\(b=a-10\)
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!
