Bài 8: Chia hai lũy thừa cùng cơ số

\(2M=2^2+2^3+2^4+...+2^{2021}\)

\(\Leftrightarrow M=2^{2021}-2\)

Câu 17

A.11k+7

Câu 18 

A. x∈ \(\left\{0,1\right\}\)

Câu 17: A

Câu 18:

$x^{15}=x^2$

$x^{15}-x^2=0$

$x^2(x^{13}-1)=0$

$\Rightarrow x^2=0$ hoặc $x^{13}-1=0$

$\Rightarrow x=0$ hoặc $x=1$

Đáp án A.

a) \(x+16⋮x+1\Leftrightarrow x+1+15⋮x+1\)

mà \(\Leftrightarrow x+1⋮x+1\Rightarrow15⋮x+1\Rightarrow x+1\inƯ\left(15\right)=\left\{\pm1;\pm3;\pm5;\pm15\right\}\Rightarrow x\in\left\{-16;-6;-4;-2;0;2;4;14\right\}\)

b) 

a) \(x+11⋮x+1\Leftrightarrow x+1+10⋮x+1\)

mà \(\Leftrightarrow x+1⋮x+1\Rightarrow10⋮x+1\Rightarrow x+1\inƯ\left(10\right)=\left\{\pm1;\pm2;\pm5;\pm10\right\}\Rightarrow x\in\left\{-11;-6;-3;-2;0;1;4;9\right\}\)

1) \(\Rightarrow\left(x+1\right)+15⋮\left(x+1\right)\)

\(\Rightarrow\left(x+1\right)\inƯ\left(15\right)=\left\{-15;-5;-3;-1;1;3;5;15\right\}\)

\(\Rightarrow x\in\left\{-16;-6;-4;-2;0;2;4;14\right\}\)

2) \(\Rightarrow\left(x+1\right)+10⋮\left(x+1\right)\)

\(\Rightarrow\left(x+1\right)\inƯ\left(10\right)=\left\{-10;-5;-2;-1;1;2;5;10\right\}\)

\(\Rightarrow x\in\left\{-11;-5;-3;-2;0;1;4;9\right\}\)

x= 7

\(14⋮2x\\ \Rightarrow7⋮x\\ \Rightarrow x\in\left\{\pm1;\pm7\right\}\)

\(\Rightarrow2x\inƯ\left(14\right)=\left\{-14;-7;-2;-1;1;2;7;14\right\}\)

\(\Rightarrow x\in\left\{-7;-\dfrac{7}{2};-1;-\dfrac{1}{2};\dfrac{1}{2};1;\dfrac{7}{2};7\right\}\)

\(=21+3^2+5=26+9=35\)

\(84:4+3^9:3^7+5=21+3^2+5=35\)

=21+9+5

=35

7776

7776 hoặc 6⁵

7776

a) \(\left(x-5\right)\left(2x-3^2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=5\\2x=9\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{9}{2}\end{matrix}\right.\)

b) \(2\left(3x-15\right)\left(5-x\right)=0\)

\(\Rightarrow6\left(x-5\right)\left(5-x\right)=0\Rightarrow x=5\)

(x - 5)(2x - 3²) = 0

=> \(\left[\begin{array}{} x - 5 = 0\\ 2x - 3^{2} = 0 \end{array} \right.\)=> \(\left[\begin{array}{} x = 0 - 5 = -5\\ 2x = 0 - 3^{2} = 0 - 9 = -9 => x = \dfrac{9}{2} \end{array} \right.\)

b) 2(3x - 15)(5 - x) = 0

      (6x - 30)(5 - x) = 0

=> \(\begin{cases} 6x - 30 = 0\\ 5 - x =0 \end{cases} \) => \(\begin{cases} 6x = 0 + 30 = 30 => x = 5\\ x = 0 + 5 = 5 \end{cases} \)

a: \(24\cdot16=2^3\cdot3\cdot2^4=2^7\cdot3\)

c: \(75:\left(7\cdot72\right)=\dfrac{3\cdot5^2}{7\cdot3^2\cdot2^2}=\dfrac{5^2}{7\cdot3\cdot2^2}\)

\(a,BC\left(2,5,15\right)=B\left(30\right)=\left\{0;30;60;90;120;...\right\}\\ \Rightarrow x\in\left\{0;30;60;90\right\}\\ b,BC\left(8,15,40\right)=B\left(120\right)=\left\{0;240;360;480;...\right\}\\ \Rightarrow x=360\)

Lời giải

Gọi số sách có là  quyển ()

Theo bài ra ta có

Mà