Toán Lớp 9: A=(2 căn x+3)/(3 căn x + 5)
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Toán Lớp 9: A=(2 căn x+3)/(3 căn x + 5)
tìm x nguyên để a nguyên
Comments ( 1 )
DK:x \ge 0\\
A = \dfrac{{2\sqrt x + 3}}{{3\sqrt x + 5}}\\
\to 3A = \dfrac{{6\sqrt x + 9}}{{3\sqrt x + 5}} = \dfrac{{2\left( {3\sqrt x + 5} \right) – 1}}{{3\sqrt x + 5}}\\
= 2 – \dfrac{1}{{3\sqrt x + 5}}\\
A \in Z \to \dfrac{1}{{3\sqrt x + 5}} \in Z\\
\to 3\sqrt x + 5 \in U\left( 1 \right)\\
\to 3\sqrt x + 5 = 1\\
\to 3\sqrt x = – 4\left( {KTM} \right)\\
\to x \in \emptyset
\end{array}\)