Question 1112295
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<pre>
The given equation 

2x^2 +(2k-1)x = k  



is equivalent to

2x^2 +(2k-1)x - k = 0



which, in turn, is factored as


(2x-1)*(x+k) = 0


and, OBVIOUSLY, has the roots  x= {{{1/2}}}  and  x= k,  that are rational numbers.
</pre>

Solved and Proved.