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?
+14913 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.
!
