Toán Lớp 8: A=x^2-x+3/x-2 tìm x sao cho A nguyên
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Toán Lớp 8: A=x^2-x+3/x-2 tìm x sao cho A nguyên
Comments ( 1 )
x = 7\\
x = – 3\\
x = 3\\
x = 1
\end{array} \right.\)
DK:x \ne 2\\
A = \dfrac{{{x^2} – x + 3}}{{x – 2}}\\
= \dfrac{{{x^2} – 2x + x – 2 + 5}}{{x – 2}}\\
= \dfrac{{x\left( {x – 2} \right) + \left( {x – 2} \right) + 5}}{{x – 2}}\\
= x + 1 + \dfrac{5}{{x – 2}}\\
A \in Z \to \dfrac{5}{{x – 2}} \in Z\\
\to x – 2 \in U\left( 5 \right)\\
\to \left[ \begin{array}{l}
x – 2 = 5\\
x – 2 = – 5\\
x – 2 = 1\\
x – 2 = – 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 7\\
x = – 3\\
x = 3\\
x = 1
\end{array} \right.
\end{array}\)