Explanation

(a)
Given, $NO_{2} \rightleftharpoons \frac{1}{2}N_{2} + O_{2},\ \ \ \ \ \ \ \ \ \ \ \ \ K_{1}$ …(i)
$N_{2}O_{4} \rightleftharpoons 2NO_{2},\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K_{2}$ …(ii)
Required reaction
$N_{2} + 2O_{2} \rightleftharpoons N_{2}O_{4},\ \ \ \ \ \ \ \ \ \ \ \ \ \ K$ …(iii)
By squaring Eq. (i) we get,
$2NO_{2} \rightleftharpoons N_{2} + {2O}_{2},\ \ \ \ \ \ \ \ \ \ \ \ \ K_{1}^{2}$ …(iv)
Now, Eq (iii) is obtained by inverting Eq. (ii) and Eq. (iv) and by adding them as.
$N_{2} + 2O_{2} \rightleftharpoons 2{NO}_{2},\ \ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{K_{1}^{2}}$
$2NO_{2} \rightleftharpoons N_{2}O_{4},\ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{K_{2}}$
---------------------------------------------------------
$N_{2} + 2O_{2} \rightleftharpoons N_{2}O_{4},\ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{K_{1}^{2}} + \frac{1}{K_{2}}$