Question

[Linh Dan Pham]

Cho B= 1/13(-65/x-7+26/x-7)

(Với x khác 7, x thuộc Z)

a, rút gọn B

b, tìm các số x nguyên để B nguyên.

Giúp mik với, mik gần gấp lắm

Answer 1

[Đức Hiếu]

a, \(B=\dfrac{1}{13}\left(\dfrac{-65}{x-7}+\dfrac{26}{x-7}\right)\)

\(=\dfrac{1}{13}\left(\dfrac{-65+26}{x-7}\right)=\dfrac{1}{13}.\dfrac{-39}{x-7}=\dfrac{-3}{x-7}=-\dfrac{3}{x-7}\)

b, Để B đạt giá trị nguyên thì \(\dfrac{3}{x-7}\) phải đạt giá trị nguyên.

\(\Rightarrow x-7\inƯ\left(3\right)\Rightarrow x-7\in\left\{-3;-1;1;3\right\}\)

\(\Rightarrow x\in\left\{4;6;8;10\right\}\)

Vậy...........

Chúc bạn học tốt!!!

Answer 2

[Mashiro Shiina]

\(B=\dfrac{1}{13}\left(\dfrac{-65}{x-7}+\dfrac{26}{x-7}\right)\)

\(B=\dfrac{-65}{13\left(x-7\right)}+\dfrac{26}{13\left(x-7\right)}\)

\(B=\dfrac{-65}{13x-91}+\dfrac{26}{13x-91}\)

\(B=\dfrac{-39}{13x-91}\)

\(B\in Z\Rightarrow\left\{{}\begin{matrix}-65⋮x-7\\26⋮x-7\end{matrix}\right.\)

\(\Rightarrow x-7\in UC\left(-65;26\right)\)

\(UCLN\left(-65;26\right)=13\)

\(\Rightarrow\left[{}\begin{matrix}x-7=13\Rightarrow x=20\\x-7=-13\Rightarrow x=-6\\x-7=1\Rightarrow x=8\\x-7=-1\Rightarrow x=6\end{matrix}\right.\)