What is the value for the reverse reaction?
${K_c}$ of reverse reaction should just be the reciprocal of forward ${K_c}$. So, ${K_c}$ of reverse reaction is $\frac{1}{1752}$. 

Now, I am not sure, why you used 2nd equation. Suppose you have 1 unit conc of $\ce{NO}$ and $\ce{O_2}$, then after time $t$, if the conversion is $x$, then your equation should be
$1752 = \frac{[2x]^2}{([1-x])^3}$. 

Can you please check your 2nd equation again?