\(x\left(x+1\right)+1\in\text{Ư}\left(3\right)\)

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

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

Vì x và x+1 là 2 số liên tiếp => x(x+1) là số chẵn 

=> x(x+1)\(\in\){ 0;-2}

Nếu x(x+1)=0=> \(\orbr{\begin{cases}x=0\\x+1=0\end{cases}}\)=>\(\orbr{\begin{cases}x=0\\x=-1\end{cases}}\)

Nếu x(x+1) =-2 => \(\orbr{\begin{cases}x=2\\x+1=-1\end{cases}}\)=> x=2 Hoặc x=-2

Hoặc 

a) Ta có: \(\frac{x}{12}=\frac{y}{3}.\)

=> \(\frac{x}{12}=\frac{y}{3}\) và \(x-y=36.\)

Áp dụng tính chất dãy tỉ số bằng nhau ta được:

\(\frac{x}{12}=\frac{y}{3}=\frac{x-y}{12-3}=\frac{36}{9}=4.\)

\(\left\{{}\begin{matrix}\frac{x}{12}=4=>x=4.12=48\\\frac{y}{3}=4=>y=4.3=12\end{matrix}\right.\)

Vậy \(\left(x;y\right)=\left(48;12\right).\)

b)

\(\frac{2}{3}+\frac{5}{3}x=\frac{5}{7}\)

⇒ \(\frac{5}{3}x=\frac{5}{7}-\frac{2}{3}\)

⇒ \(\frac{5}{3}x=\frac{1}{21}\)

⇒ \(x=\frac{1}{21}:\frac{5}{3}\)

⇒ \(x=\frac{1}{35}\)

Vậy \(x=\frac{1}{35}.\)

\(\left(x-\frac{1}{2}\right)^3=\frac{1}{27}\)

⇒ \(\left(x-\frac{1}{2}\right)^3=\left(\frac{1}{3}\right)^3\)

⇒ \(x-\frac{1}{2}=\frac{1}{3}\)

⇒ \(x=\frac{1}{3}+\frac{1}{2}\)

⇒ \(x=\frac{5}{6}\)

Vậy \(x=\frac{5}{6}.\)

Có 1 câu bạn đăng mình làm ở dưới rồi mà.

Chúc bạn học tốt!

a)áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{x}{12}=\frac{y}{3}=\frac{x-y}{12-3}=\frac{36}{9}=4\)

\(\)x/12=4 suy ra x=12.4=48

y/3=4 suy ra y=3.4 =12

b)\(\frac{2}{3}+\frac{5}{3}x=\frac{5}{7}\)

\(\frac{5}{3}x=\frac{5}{7}-\frac{2}{3}\)

\(\frac{5}{3}x=\frac{1}{21}\)

\(x=\frac{1}{21}:\frac{5}{3}\)

\(x=\frac{1}{35}\)

\(\frac{11}{12}-\left(\frac{2}{5}+x\right)=\frac{2}{3}\)

\(\left(\frac{2}{5}+x\right)=\frac{11}{12}-\frac{2}{3}\)

\(\frac{2}{5}+x=\frac{1}{4}\)

\(x=\frac{1}{4}-\frac{2}{5}\)

\(x=\frac{-3}{20}\)

\(\left|x-\frac{2}{5}\right|+\frac{3}{4}=\frac{11}{4}\)

\(\left|x-\frac{2}{5}\right|=\frac{11}{4}-\frac{3}{4}\)

\(\left|x-\frac{2}{5}\right|=2\)

suy ra x-2/5=2 hoac x-2/5=-2

\(x-\frac{2}{5}=2\)

\(x=\frac{12}{5}\)

\(x-\frac{2}{5}=-2\)

\(x=\frac{-8}{5}\)

\(\left(x-\frac{1}{2}\right)^3=\frac{1}{27}\)

\(\left(x-\frac{1}{2}\right)^3=\left(\frac{1}{3}\right)^3\)

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

\(x=\frac{1}{3}+\frac{1}{2}\)

\(x=\frac{5}{6}\)

a)tìm x,y biết:$\frac{x}{12}=\frac{y}{3}vàx-y=36$

Ta có : \(\dfrac{x}{12} = \dfrac{y}{3}\) \(\Rightarrow\) \(\dfrac{x-y}{12-3} = \dfrac{36}{9} = 4\)

b)tìm x biết:

$\frac{2}{3}+\frac{5}{3}x=\frac{5}{7}$

\(\Leftrightarrow\) \(\dfrac{5}{3}x = \dfrac{5}{7} - \dfrac{2}{3}\)

\(\Leftrightarrow\) \(\dfrac{5}{3}x = \dfrac{1}{21}\)

\(\Leftrightarrow\) \(x = \dfrac{1}{35}\)

$\frac{11}{12}-\left(\frac{2}{5}+x\right)=\frac{2}{3}$

\(\Leftrightarrow\) \(\dfrac{2}{5} +x\) = \(\dfrac{2}{3} - \dfrac{11}{12}\)

\(\Leftrightarrow\) \(\dfrac{2}{5} + x = \dfrac{-1}{4}\)

\(\Leftrightarrow\) \(x = \dfrac{-13}{20}\)

$\left|x-\frac{2}{5}\right|+\frac{3}{4}=\frac{11}{4}$

\(\Leftrightarrow\) \(x - \dfrac{2}{5} = 2\)

\(\Leftrightarrow\) \(x = \dfrac{8}{5}\)

${\left(x-\frac{1}{2}\right)}^3=\frac{1}{27}$

\(\Leftrightarrow\) \(x - \dfrac{1}{2} = \dfrac{1}{19683}\)

\(\Leftrightarrow\) \(x = \dfrac{19685}{39366}\)

\(\frac{|x-2|}{12}\)\(+\)\(\frac{|x-2|}{20}+\)\(\frac{|x-2|}{30}+\)\(\frac{|x-2|}{42}\)\(=\frac{70^5}{2^3.21^6}\)

\(\Rightarrow|x-2|.\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)=\frac{2^5.5^5.7^5}{2^3.7^6.3^6}\)

\(\Rightarrow|x-2|.\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)=\frac{2^2.5^5}{7.3^6}\)

\(\Rightarrow|x-2|.\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)=\frac{4.5^5}{21.3^5}\)

\(\Rightarrow|x-2|\left(\frac{1}{3}-\frac{1}{7}\right)=\frac{4.5^5}{21.3^5}\)\(\Rightarrow|x-2|=\frac{5^5}{3^5}\)

ĐẾN ĐÂY DỄ RÙI TỰ GIẢI TIẾP

x thuộc Z

\(\left(x-2\right):\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)

\(\left(x-2\right):\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\left(x-2\right):\frac{2}{9}=\frac{16}{9}\)

\(x-2=\frac{32}{91}\)

\(x=\frac{32}{91}+2\)

\(x=\frac{212}{91}\)