Question

8a + 19 : 4a +1 có giá trị là nguyên

 

Answer 1

Giải:

Để 8a + 19 : 4a + 1 có giá trị nguyên

\(\Rightarrow8a+19⋮4a+1\)

Ta có: \(8a+19⋮4a+1\)

\(\Rightarrow\left(8a+2\right)+17⋮4a+1\)

\(\Rightarrow2\left(4a+1\right)+17⋮4a+1\)

\(\Rightarrow17⋮4a+1\)

\(\Rightarrow4a+1\in\left\{1;-1;3;-3\right\}\)

+) \(4a+1=1\Rightarrow a=0\)

+) \(4a+1=-1\Rightarrow a=\frac{-1}{2}\)

+) \(4a+1=3\Rightarrow a=\frac{1}{2}\)

+) \(4a+1=-3\Rightarrow a=-1\)

Vậy \(a\in\left\{0;\frac{-1}{2};\frac{1}{2};-1\right\}\)