Tất cả các phần trên đều thuộc dạng ước chung.

a) \(A\inƯC\left(420;700\right)\)

b) \(A\inƯC\left(480;600\right)\)

c) \(A\inƯC\left(105;175;385\right)\)

d) \(A\inƯC\left(548;638\right)\)

Sau 1 giờ vòi chảy được:

1/3+1/5+1/6=10/30+6/30+5/30=7/10(bể)

Sau 1 giờ thì bể còn:

1-7/10=3/10(bể không chứa nước)

Để A > -2 thì :

=> \(\sqrt{x}-x>-2\)

⇔ \(\sqrt{x}\left(1-\sqrt{x}\right)>-2\)

⇔\(\left\{{}\begin{matrix}\sqrt{x}>-2\\1-\sqrt{x}>-2\\\sqrt{x}< -2\\1-\sqrt{x}< -2\end{matrix}\right.\)  ⇔\(\left\{{}\begin{matrix}x>4\\x< 9\\x< 4\\x>9\end{matrix}\right.\) ⇔\(\left\{{}\begin{matrix}x>9\\x< 4\end{matrix}\right.\)

nếu mình sai thì sửa sau :>

Để A>-2 thì \(-x+\sqrt{x}+2>0\)

\(\Leftrightarrow x-\sqrt{x}-2>0\)

=>x>4

\(3n+14⋮n+2\)

=>\(3n+6+8⋮n+2\)

=>\(8⋮n+2\)

=>\(n+2\in\left\{1;-1;2;-2;4;-4;8;-8\right\}\)

=>\(n\in\left\{-1;-3;0;-4;2;-6;6;-10\right\}\)

mà n>=0

nên \(n\in\left\{0;2;6\right\}\)

\(A=\left(1+2+2^2\right)+\left(2^3+2^4+2^5\right)+...+\left(2^{27}+2^{28}+2^{29}\right)\\ A=\left(1+2+2^2\right)+2^3\left(1+2+2^2\right)+...+2^{27}\left(1+2+2^2\right)\\ A=\left(1+2+2^2\right)\left(1+2^3+...+2^{27}\right)\\ A=7\left(1+2^3+...+2^{27}\right)⋮7\)

\(A=2+2^2+...+2^{60}\)

\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)

\(A=2\cdot3+2^3\cdot3+...+2^{59}\cdot3\)

\(A=3\cdot\left(2+2^3+...+2^{59}\right)\)

Vậy A chia hết cho 3 

_______________

\(A=2+2^2+2^3+...+2^{60}\)

\(A=\left(2+2^3\right)+\left(2^2+2^4\right)+...+\left(2^{58}+2^{60}\right)\)

\(A=2\cdot5+2^2\cdot5+...+2^{58}\cdot5\)

\(A=5\cdot\left(2+2^2+...+2^{58}\right)\)

Vậy A ⋮ 5

___________________

\(A=2+2^2+2^3+...+2^{60}\)

\(A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\)

\(A=2\cdot7+2^4\cdot7+...+2^{58}\cdot7\)

\(A=7\cdot\left(2+2^4+...+2^{58}\right)\)

Vậy A ⋮ 7 

Có \(A=\left(2n+2\right).\left(4n+8\right)=8.\left(n+1\right).\left(n+2\right)\)

Lại có n + 1 , n + 2 là 2 số tự nhiên liên tiếp 

nên (n + 1).(n + 2) \(⋮2\forall n\inℕ\)

\(\Leftrightarrow A=8\left(n+1\right)\left(n+2\right)⋮16\)