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# math

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123
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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
+179
0

I got 0 with 0 and 10

Jan 7, 2022
#3
+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
+13716
+1

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

Hello Guest!!

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

!

Jan 7, 2022
#4
+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