$\begin{array}{l} 2022\sqrt {2022x - 2021} + \sqrt {2023x - 2022} = 2023\\ \Leftrightarrow \left( {2022\sqrt {2022x - 2021} - 2022} \right) + \left( {\sqrt {2023x - 2022} - 1} \right) = 0\\ \Leftrightarrow 2022\left( {\sqrt {2022x - 2021} - 1} \right) + \left( {\sqrt {2023x - 2022} - 1} \right) = 0\\ \Leftrightarrow 2022.\dfrac{{2022x - 2022}}{{\sqrt {2022x - 2021} + 1}} + \dfrac{{2023x - 2023}}{{\sqrt {2023x - 2022} + 1}} = 0\\ \Leftrightarrow {2022^2}.\dfrac{{x - 1}}{{\sqrt {2022x - 2021} + 1}} + 2023.\dfrac{{\left( {x - 1} \right)}}{{\sqrt {2023x - 2022} + 1}} = 0\\ \Leftrightarrow \left( {x - 1} \right)\left( {\underbrace {\dfrac{{{{2022}^2}}}{{\sqrt {2022x - 2021} + 1}} + \dfrac{{2023}}{{\sqrt {2023x - 2022} + 1}}}_{ > 0}} \right) = 0\\ \Leftrightarrow x - 1 = 0\\ \Leftrightarrow x = 1 \Rightarrow S = \left\{ 1 \right\} \end{array}$
