9.3. Find the value of the expression $x-\sqrt{2022 x}+2023$,

if $x-\sqrt{\frac{2022}{x}}=2023$.
Answer: 2024.

Solution. Transform the condition $x-\sqrt{\frac{2022}{x}}=2023$ given that $x>0$. We get: $x^{2}-\sqrt{2022 x}=2023 x ; x^{2}-2022 x-x-\sqrt{2022 x}=0$;

$$
(x-\sqrt{2022 x})(x+\sqrt{2022 x})-(x+\sqrt{2022 x});(x-\sqrt{2022 x}-1)(x+
$$

$\sqrt{2022 x})=0$.

The second factor is positive for all $x>0$, which implies that $x-$ $\sqrt{2022 x}-1=0$, from which $x-\sqrt{2022 x}+2023=2024$.