Bài 1 :                                                                        Bài giải

\(\frac{28^{15}\cdot3^{17}}{84^{16}}=\frac{\left(2^2\cdot7\right)^{15}\cdot3^{17}}{\left(2^2\cdot3\cdot7\right)^{16}}=\frac{2^{30}\cdot7^{15}\cdot3^{17}}{2^{32}\cdot3^{16}\cdot7^{16}}=\frac{3}{2^2\cdot7}=\frac{3}{4\cdot7}=\frac{3}{28}\)

Bài 2 :                                                              Bài giải

\(\frac{3^6\cdot21^{12}}{175^9\cdot7^3}=\frac{3^6\cdot\left(3\cdot7\right)^{12}}{\left(5^2\cdot7\right)^9\cdot7^3}=\frac{3^6\cdot3^{12}\cdot7^{12}}{5^{18}\cdot7^9\cdot7^3}=\frac{3^{18}\cdot7^{12}}{5^{18}\cdot7^{12}}=\frac{3^{18}}{5^{18}}\)

\(\frac{3^{10}\cdot6^7\cdot4}{10^9\cdot5^8}=\frac{3^{10}\cdot\left(2\cdot3\right)^7\cdot2^2}{\left(2\cdot5\right)^9\cdot5^8}=\frac{3^{10}\cdot2^7\cdot3^7\cdot2^2}{2^9\cdot5^9\cdot5^8}=\frac{3^{17}\cdot2^9}{2^9\cdot5^{17}}=\frac{3^{17}}{5^{17}}\)

Ta có : \(3^{17}\cdot5^{18}=3^{17}\cdot5^{17}\cdot5=\left(3\cdot5\right)^{17}\cdot5=15^{17}\cdot5\)

\(3^{18}\cdot5^{17}=3\cdot3^{17}\cdot5^{17}=3\cdot\left(3\cdot5\right)^{17}=3\cdot15^{17}\)

\(\text{ Vì }5\cdot15^{17}>3\cdot15^{17}\text{ }\Rightarrow\text{ }3^{17}\cdot5^{18}>3^{18}\cdot5^{17}\text{ }\Rightarrow\text{ }\frac{3^{18}}{5^{18}}< \frac{3^{17}}{5^{17}}\)

cảm ơn nha

a) \(||2x-3|-4x|=5\)

TH1: \(|2x-3|-4x=5\)

\(\Leftrightarrow|2x-3|=5+4x\)

\(\Leftrightarrow\orbr{\begin{cases}2x-3=5+4x\\2x-3=-5-4x\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x-4x=5+3\\2x+4x=-5+3\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}-2x=8\\6x=-2\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=-4\\x=\frac{-1}{3}\end{cases}}\)

TH2: \(|2x-3|-4x=-5\)

\(\Leftrightarrow|2x-3|=-5-4x\)<0 ( loại )

Vậy \(x\in\left\{-4;\frac{-1}{3}\right\}\)

phần a tui làm sairooif để làm lại

\(\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{a^2}< \frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{\left(a-1\right)a}\left(2^2>1.2;...;a^2>a\left(a-1\right)\right)=1-\frac{1}{a}< 1\)

Trả lời:

Bài 1 : \(\text{(3x - 5)=4}\)

         \(\text{3x - 5=4}\)

         \(\text{3x =4+5}\)

         \(\text{3x =9}\)

          \(x=\frac{9}{3}\)

         \(x=3\)

Vậy    \(x=3\)

~ Học tốt ~

Bài 2:

a) A = \(\frac{3n+9}{n-4}\)

Để \(\frac{3n+9}{n-4}\) có giá trị là 1 số nguyên thì:

\(3n+9⋮n-4\)

hay \(3n-12+21⋮n-4\)

  \(3.\left(n-4\right)+21⋮n-4\)

\(\Rightarrow21⋮n-4\) ( vì \(3.\left(n-4\right)⋮n-4\)

\(\Rightarrow n-4\in\left\{\pm1;\pm3;\pm7;\pm21\right\}\)

\(\Rightarrow n\in\left\{5;3;7;1;11;-3;25;-17\right\}\)

Vậy   \(n\in\left\{5;3;7;1;11;-3;25;-17\right\}\)

~ Học tốt ~

=> (6x-2)*5y=(3x+1)*(8y-6)

bn làm nốt nhé

a) \(\left|x\left(x-4\right)\right|=2x\)\(\left(x\ge0\right)\)(1)

Nếu \(x\ge4\)thì \(\left|x\left(x-4\right)\right|=x\left(x-4\right)\)

\(\Rightarrow\left(1\right)\Leftrightarrow x^2-4x=2x\Leftrightarrow x^2-6x=0\)

\(\Leftrightarrow x\left(x-6\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x=6\end{cases}}\)

Nếu \(0\le x< 4\)thì \(\left|x\left(x-4\right)\right|=x\left(4-x\right)\)

\(\Rightarrow\left(1\right)\Leftrightarrow4x-x^2=2x\Leftrightarrow2x-x^2=0\)

\(\Leftrightarrow x\left(2-x\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\)

Vậy \(x\in\left\{0;2;6\right\}\)

\(\left|x-1\right|\ge0;\left|x-2\right|\ge0;\left|x-3\right|\ge0\)

\(\Rightarrow VT\ge0\Rightarrow1-2x\ge0\Leftrightarrow x\le\frac{1}{2}\)

\(\Rightarrow\hept{\begin{cases}\left|x-1\right|=1-x\\\left|x-2\right|=2-x\\\left|x-3\right|=3-x\end{cases}}\)

\(\Rightarrow pt\Leftrightarrow6-3x=1-2x\)

\(\Leftrightarrow x=5\left(KTM\right)\)

Vậy pt vô nghiệm