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If a and b are positive integers for which ab-6a+5b=15, what is the minimal possible value of |a-b|?

 Jan 5, 2022
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What is the minimal possible value of |a-b|?

 

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\(ab-6a+5b=15\\ b(a+5)-6a=15\\ b=\frac{15+6a}{5+a}\)

\({\color{blue}5}=\dfrac{15+6\cdot {\color{blue}10}}{5+{\color{blue}10}}\)

The minimal possible value of |a-b| is 5.

laugh  !
 

 Jan 5, 2022
edited by asinus  Jan 5, 2022

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