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

 Jan 7, 2022
 #1
avatar+179 
0

I got 0 with 0 and 10

 Jan 7, 2022
 #3
avatar+675 
0

There are not just natural numbers, but also negative numbers.

When the description is saying "are integers" then you can use for a and b natural + negative values. 

Straight  Jan 7, 2022
 #2
avatar+13716 
+1

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

 

Hello Guest!!

 

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

laugh  !

 Jan 7, 2022
 #4
avatar+360 
+1

\(a-b=10\)

\(b=a-10\)

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!

 Jan 7, 2022

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