Giải thích các bước giải:
4.Để $\dfrac{6}{x+1}\cdot \dfrac{x-1}{3}\in Z$
$\to \dfrac{2(x-1)}{x+1}\in Z$
$\to 2(x-1)\quad\vdots\quad x+1$
$\to 2(x+1-2)\quad\vdots\quad x+1$
$\to 2(x+1)-4\quad\vdots\quad x+1$
$\to 4\quad\vdots\quad x+1$
$\to x+1\in U(4)$
$\to x+1\in\{1, 2, 4, -1, -2, -4\}$
$\to x\in\{0, 1, 3, -2, -3, -5\}$
Bài 5:
Ta có $\dfrac{x}{5}=\dfrac{y}{9}$
$\to x=\dfrac59y$
$\to xy=\dfrac59y^2$
$\to 405=\dfrac59y^2$
$\to y^2=729$
$\to y=27\to x=15$
Hoặc $y=-27\to x=-15$
Bài 6:
a.Ta có:
$\dfrac{1}{27}\cdot 81^n=3^n$
$\to \dfrac{1}{3^3}\cdot (3^4)^n=3^n$
$\to \dfrac{1}{3^3}\cdot 3^{4n}=3^n$
$\to 3^{4n-3}=3^n$
$\to 4n-3=n$
$\to 3n=3$
$\to n=1$
b.Ta có:
$8<2^n<64$
$\to 2^3< 2^n< 2^6$
$\to 3< n< 6$
Mà $n\in Z^+$
$\to n\in\{4, 5\}$
