Question

tìm n∈ Z để A∈ Z

A= \(\frac{12}{3n-1}\)

Answer 1

Lập bảng \(\frac{12}{3n-1}\)là số nguyên

=> 12\(⋮\)3n-1 \(\in\)Ư( 12)={1;-1;-2;2;-3;3;-4;4;-;6;-12;12}

3n-1	1	-1	2	-2	3	-3	4	-4	6	-6	12	-12
n	2/3	0	1	-1/3	4/3	-2/3	5/3	-1	7/3	-5/3	13/3	-11/3

Vì n thuộc Z nên ...

Answer 2

Để A ∈ Z thì

12 ⋮ 3n - 1 ⇒ 3n - 1 ∈ Ư(12) = \(\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\right\}\)

⇒ n ∈ \(\left\{\frac{2}{3};0;1;-\frac{1}{3};\frac{4}{3};-\frac{2}{3};\frac{5}{3};-1;\frac{7}{3};-\frac{5}{3};\frac{13}{3};-\frac{11}{3}\right\}\)

Hay n ∈ \(\left\{\pm\frac{2}{3};0;\pm1;-\frac{1}{3};\frac{4}{3};\pm\frac{5}{3};\frac{7}{3};\frac{13}{3};-\frac{11}{3}\right\}\)