Đáp án:
3) x=196
Giải thích các bước giải:
\(\begin{array}{l}
1)DK:x \ge 0;x \ne 1\\
Q = \dfrac{{15\sqrt x - 11 - \left( {3\sqrt x - 2} \right)\left( {\sqrt x + 3} \right) - \left( {2\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 3} \right)}}\\
= \dfrac{{15\sqrt x - 11 - 3x - 7\sqrt x + 6 - 2x - \sqrt x + 3}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 3} \right)}}\\
= \dfrac{{ - 5x + 7\sqrt x - 2}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 3} \right)}}\\
= \dfrac{{\left( {\sqrt x - 1} \right)\left( {2 - 5\sqrt x } \right)}}{{\left( {\sqrt x - 1} \right)\left( {\sqrt x + 3} \right)}}\\
= \dfrac{{2 - 5\sqrt x }}{{\sqrt x + 3}}\\
2)Q = \dfrac{1}{2}\\
\to \dfrac{{2 - 5\sqrt x }}{{\sqrt x + 3}} = \dfrac{1}{2}\\
\to 4 - 10\sqrt x = \sqrt x + 3\\
\to 11\sqrt x = 1\\
\to x = \dfrac{1}{{121}}\\
3)Q = \dfrac{{2 - 5\sqrt x }}{{\sqrt x + 3}} = \dfrac{{ - 5\left( {\sqrt x + 3} \right) + 17}}{{\sqrt x + 3}} = - 5 + \dfrac{{17}}{{\sqrt x + 3}}\\
Q \in Z \to \dfrac{{17}}{{\sqrt x + 3}} \in Z\\
\to \sqrt x + 3 \in U\left( {17} \right)\\
\to \left[ \begin{array}{l}
\sqrt x + 3 = 17\\
\sqrt x + 3 = 1
\end{array} \right. \to \left[ \begin{array}{l}
\sqrt x = 14\\
\sqrt x = - 2\left( l \right)
\end{array} \right.\\
\to x = 196
\end{array}\)
( phần 4 không thấy đề bạn )
