Đáp án:
x=9
Giải thích các bước giải:
\(\begin{array}{l}
B = \dfrac{{x + 2\sqrt x + 3\sqrt x - 6 - 9\sqrt x + 10}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x - 2} \right)}}\\
= \dfrac{{x - 4\sqrt x + 4}}{{\left( {\sqrt x + 2} \right)\left( {\sqrt x - 2} \right)}}\\
= \dfrac{{\sqrt x - 2}}{{\sqrt x + 2}}\\
P = B:A = \dfrac{{\sqrt x - 2}}{{\sqrt x + 2}}:\dfrac{{\sqrt x - 2}}{{\sqrt x - 3}}\\
= \dfrac{{\sqrt x - 3}}{{\sqrt x + 2}} = \dfrac{{\sqrt x + 2 - 5}}{{\sqrt x + 2}} = 1 - \dfrac{5}{{\sqrt x + 2}}\\
P \in Z\\
\to \dfrac{5}{{\sqrt x + 2}} \in Z\\
\to \sqrt x + 2 \in U\left( 5 \right)\\
\to \left[ \begin{array}{l}
\sqrt x + 2 = 5\\
\sqrt x + 2 = 1\left( l \right)
\end{array} \right.\\
\to \sqrt x = 3\\
\to x = 9
\end{array}\)
