Đáp án:
\(\left[ \begin{array}{l}
x = 49\\
x = 9\\
x = 36\\
x = 16
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
A = \dfrac{{\sqrt x - 5 + \sqrt x + 5}}{{\left( {\sqrt x + 5} \right)\left( {\sqrt x - 5} \right)}}.\dfrac{{\sqrt x + 5}}{{\sqrt x }}\\
= \dfrac{{2\sqrt x }}{{\left( {\sqrt x + 5} \right)\left( {\sqrt x - 5} \right)}}.\dfrac{{\sqrt x + 5}}{{\sqrt x }}\\
= \dfrac{2}{{\sqrt x - 5}}\\
A \in Z \to \dfrac{2}{{\sqrt x - 5}} \in Z\\
\to \sqrt x - 5 \in U\left( 2 \right)\\
\to \left[ \begin{array}{l}
\sqrt x - 5 = 2\\
\sqrt x - 5 = - 2\\
\sqrt x - 5 = 1\\
\sqrt x - 5 = - 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
\sqrt x = 7\\
\sqrt x = 3\\
\sqrt x = 6\\
\sqrt x = 4
\end{array} \right. \to \left[ \begin{array}{l}
x = 49\\
x = 9\\
x = 36\\
x = 16
\end{array} \right.
\end{array}\)
