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In the equation 1/j + 1/k = 2/3, both j and k are positive integers. What is the sum of all possible values for k?

 Aug 16, 2021
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In the equation 1/j + 1/k = 2/3, both j and k are positive integers. What is the sum of all possible values for k?

 

Hello Guest!

 

1/j + 1/k = 2/3

\( \frac{1}{k}=\frac{2}{3}-\frac{1}{j}\\ \frac{1}{k}=\frac{2j-3}{3j}\\ \color{blue}k=\frac{3j}{2j-3}\)

\(j\in\{\)  0,  1,  2,  3 \(\}\)

\(k\in\{\)  0, -2,  4,  2 \(\}\)

 

The sum of all possible values for k is 4.

laugh  !


 

 Aug 16, 2021

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