Question

tìm giá trị ngyên của x để viểu thức sau có giá trị nguyên a)A=5/x-1 b)B=X-3/x-4 c)C=3x-2/x+5

 

Answer 1

a) \(A=\dfrac{5}{x-1}\in Z\)

\(\Rightarrow\left(x-1\right)\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\)

\(\Rightarrow x\in\left\{-4;0;2;6\right\}\)

b) \(B=\dfrac{x-3}{x-4}=1+\dfrac{1}{x-4}\in Z\)

\(\Rightarrow\left(x-4\right)\inƯ\left(1\right)=\left\{-1;1\right\}\)

\(\Rightarrow x\in\left\{3;5\right\}\)

c) \(C=\dfrac{3x-2}{x+5}=\dfrac{3\left(x+5\right)}{x+5}-\dfrac{17}{x+5}=3-\dfrac{17}{x+5}\in Z\)

\(\Rightarrow\left(x+5\right)\inƯ\left(17\right)=\left\{-17;-1;1;17\right\}\)

\(\Rightarrow x\in\left\{-22;-6;-4;12\right\}\)