Đáp án:
x=16
Giải thích các bước giải:
\(\begin{array}{l}
B = \left[ {\dfrac{{15 - \sqrt x + 2\sqrt x - 10}}{{\left( {\sqrt x + 5} \right)\left( {\sqrt x - 5} \right)}}} \right].\dfrac{{\sqrt x - 5}}{{\sqrt x + 3}}\\
= \dfrac{{\sqrt x + 5}}{{\left( {\sqrt x + 5} \right)\left( {\sqrt x - 5} \right)}}.\dfrac{{\sqrt x - 5}}{{\sqrt x + 3}}\\
= \dfrac{1}{{\sqrt x + 3}}\\
M = A - B = \dfrac{{2\sqrt x }}{{\sqrt x + 3}} - \dfrac{1}{{\sqrt x + 3}}\\
= \dfrac{{2\sqrt x - 1}}{{\sqrt x + 3}} = \dfrac{{2\left( {\sqrt x + 3} \right) - 7}}{{\sqrt x + 3}}\\
= 2 - \dfrac{7}{{\sqrt x + 3}}\\
M \in Z\\
\to \dfrac{7}{{\sqrt x + 3}} \in Z\\
\to \sqrt x + 3 \in U\left( 7 \right)\\
\to \left[ \begin{array}{l}
\sqrt x + 3 = 7\\
\sqrt x + 3 = 1\left( l \right)
\end{array} \right.\\
\to \sqrt x = 4\\
\to x = 16\\
\to M = 2 - \dfrac{7}{{\sqrt {16} + 3}} = 1
\end{array}\)
