Toán Lớp 9: MỌIII NGƯỜIIII GIÚP VỚIIIIIIIII
A = ( 2x ) / ( căn x – 1 )
Tìm x nguyên để A nguyên.
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 9: MỌIII NGƯỜIIII GIÚP VỚIIIIIIIII
A = ( 2x ) / ( căn x – 1 )
Tìm x nguyên để A nguyên.
Comments ( 1 )
x = 9\\
x = 4\\
x = 0
\end{array} \right.\)
DK:x \ge 0;x \ne 1\\
A = \dfrac{{2x}}{{\sqrt x – 1}} = \dfrac{{2\left( {x – 1} \right) + 2}}{{\sqrt x – 1}}\\
= \dfrac{{2\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right) + 2}}{{\sqrt x – 1}}\\
= 2\left( {\sqrt x + 1} \right) + \dfrac{2}{{\sqrt x – 1}}\\
A \in Z \to \dfrac{2}{{\sqrt x – 1}} \in Z\\
\to \sqrt x – 1 \in U\left( 2 \right)\\
\to \left[ \begin{array}{l}
\sqrt x – 1 = 2\\
\sqrt x – 1 = 1\\
\sqrt x – 1 = – 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 9\\
x = 4\\
x = 0
\end{array} \right.
\end{array}\)