For which positive integer values of \(k\) does \(kx^2+20x+k\) have rational solutions? Express your answers separated by commas and in increasing order.

This is not a off topic post, i just accidently clicked it.

It's fine.

For rational solutions b^2-4ac must be a perfect square

\(b^2-4ac=20^2-4k^2\\ b^2-4ac=400-4k^2\\ b^2-4ac=4(100-k^2)\\ \)

so 100 - k^2 must be a perfect square

k=6, 8 are the only 2 that work.

100-36=64

100-64=36

Thank you melody :D