Toán Lớp 7: B= $\frac{x^2-2x+6}{x+1}$ tìm x để B có giá trị 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 7: B= $\frac{x^2-2x+6}{x+1}$ tìm x để B có giá trị nguyên
Comments ( 1 )
B = \dfrac{{{x^2} – 2x + 6}}{{x + 1}}\\
= \dfrac{{{x^2} + x – 3x – 3 + 9}}{{x + 1}}\\
= \dfrac{{x\left( {x + 1} \right) – 3\left( {x + 1} \right) + 9}}{{x + 1}}\\
= \dfrac{{\left( {x + 1} \right)\left( {x – 3} \right) + 9}}{{x + 1}}\\
= x – 3 + \dfrac{9}{{x + 1}}\\
B \in Z\\
\Leftrightarrow \dfrac{9}{{x + 1}} \in Z\\
\Leftrightarrow \left( {x + 1} \right) \in \left\{ { – 9; – 3; – 1;1;3;9} \right\}\\
\Leftrightarrow x \in \left\{ { – 10; – 4; – 2;0;2;8} \right\}\\
Vậy\,x \in \left\{ { – 10; – 4; – 2;0;2;8} \right\}
\end{array}$