Vì : \(\left|x-3\right|\ge0\forall x\)

\(\left|y+5\right|\ge0\forall y\)

\(\Rightarrow\left|x-3\right|+\left|y+5\right|\ge0\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}\left|x-3\right|=0\\\left|y+5\right|=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-3=0\\y+5=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-5\end{matrix}\right.\)

Vậy ....

Vì : \(\dfrac{4-x}{2x-\dfrac{1}{5}}>0\)

\(\Rightarrow4-x\) và \(2x-\dfrac{1}{5}\) là hai số cùng dấu

+)\(\Rightarrow\left\{{}\begin{matrix}4-x>0\\2x-\dfrac{1}{5}>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}-x>-4\\2x>\dfrac{1}{5}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< 4\\x>\dfrac{1}{10}\end{matrix}\right.\)

\(\Rightarrow x\in\left\{3;2;1\right\}\)

+)\(\Rightarrow\left\{{}\begin{matrix}4-x< 0\\2x-\dfrac{1}{5}< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}-x< -4\\2x< \dfrac{1}{5}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>4\\x< \dfrac{1}{10}\end{matrix}\right.\)

\(\Rightarrow\) loại

Vậy \(x\in\left\{3;2;1\right\}\)

Vì : \(2n+1⋮2n+1\Rightarrow2\left(2n+1\right)⋮2n+1\Rightarrow4n+2⋮2n+1\)

Mà : \(4n+3⋮2n+1\)

\(\Rightarrow\left(4n+3\right)-\left(4n+2\right)⋮2n+1\)

\(\Rightarrow4n+3-4n-2⋮2n+1\)

\(\Rightarrow1⋮2n+1\Rightarrow2n+1=1\Rightarrow n=0\)

Vậy n = 0 thỏa mãn

Bài 1 :

Gọi d là ước chung của 2n + 1 và 3n + 2 ( \(d\in Z;d\ne0\) )

\(\Rightarrow\left\{{}\begin{matrix}2n+1⋮d\\3n+2⋮d\end{matrix}\right.\)

Vì \(2n+1⋮d\Rightarrow3\left(2n+1\right)⋮d\Rightarrow6n+3⋮d\)

Vì \(3n+2⋮d\Rightarrow2\left(3n+2\right)⋮d\Rightarrow6n+4⋮d\)

\(\Rightarrow\left(6n+4\right)-\left(6n+3\right)⋮d\)

\(\Rightarrow6n+4-6n-3⋮d\Rightarrow1⋮d\)

\(\Rightarrow d\in\left\{-1;1\right\}\)

Vậy \(\dfrac{2n+1}{3n+2}\) là phân số tối giản

Bài 2 : thiếu đề ?

Bài 3 :

Để A nguyên \(\Rightarrow2⋮n-1\Rightarrow n-1\) thuộc ước của 2

\(\Rightarrow n-1\in\left\{1;-1;-2;2\right\}\Rightarrow n\in\left\{2;0;-1;3\right\}\)

Vậy \(n\in\left\{2;0;-1;3\right\}\) thì A nguyên

a, \(\left(4,5-2x\right)\div\dfrac{3}{4}=1\dfrac{1}{3}\)

\(\dfrac{9}{2}-2x=\dfrac{4}{3}.\dfrac{3}{4}\)

\(\dfrac{9}{2}-2x=1\Rightarrow2x=\dfrac{9}{2}-1\)

\(\Rightarrow2x=\dfrac{7}{2}\Rightarrow x=\dfrac{7}{2}\div2=\dfrac{7}{4}\)

Vậy x = \(\dfrac{7}{4}\)

b, \(\dfrac{1}{2}-\left(\dfrac{2}{3}x-\dfrac{1}{3}\right)=\dfrac{2}{3}\)

\(\dfrac{2}{3}x-\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{2}{3}\)

\(\dfrac{2}{3}x-\dfrac{1}{3}=\dfrac{-1}{6}\)

\(\dfrac{2}{3}x=\dfrac{-1}{6}+\dfrac{1}{3}\Rightarrow\dfrac{2}{3}x=\dfrac{1}{6}\)

\(x=\dfrac{1}{6}\div\dfrac{2}{3}=\dfrac{1}{6}.\dfrac{3}{2}=\dfrac{1}{4}\)

Vậy \(x=\dfrac{1}{4}\)

B =  64³.4³.16 = (4³)³.4³.4² = 4⁹.4³.4² = 4¹⁴

C = 81²:(3².27) = (3⁴)²:(3².3³) = 3⁸:3².3³ = 3⁹

D = ( 8¹¹.3¹⁷ ) : ( 27¹⁰.9¹⁵ ) = (3⁴)¹¹.3¹⁷ : (3³)¹⁰.(3²)¹⁵ = 3⁴⁴.3¹⁷:3³⁰.3³⁰ = 3⁶¹

bn đăng từ từ mn ns lm đc