Số 0 nha bn !

\(\frac{1}{2}-\left(\frac{1}{3}+\frac{3}{4}\right)\le x\le\frac{1}{24}-\left(\frac{1}{8}-\frac{1}{3}\right)\)

\(\Rightarrow\frac{1}{2}-\frac{13}{12}\le x\le\frac{1}{24}-\left(-\frac{5}{24}\right)\)

\(\Rightarrow\frac{6}{12}-\frac{13}{12}\le x\le\frac{1}{4}\)

\(\Rightarrow\frac{-7}{12}\le x\le\frac{3}{12}\)

\(\Rightarrow x\in\left\{-7;-6;-5;...;0;1;2;3\right\}\)

\(\frac{1}{2}-\left(\frac{1}{3}+\frac{3}{4}\right)\le x\le\frac{1}{24}-\left(\frac{1}{8}-\frac{1}{3}\right)\)

\(\Rightarrow\frac{1}{2}-\frac{1}{3}-\frac{3}{4}\le x\le\frac{1}{24}-\frac{1}{8}+\frac{1}{3}\)

\(\Rightarrow\frac{6-4-9}{12}\le x\le\frac{1-3+8}{24}\)

\(\Rightarrow\frac{-7}{12}\le x\le\frac{6}{24}\)

\(\Rightarrow\frac{-7}{12}\le x\le\frac{1}{4}\)

\(\Rightarrow\frac{-7}{12}\le x\le\frac{3}{12}\)

\(\Rightarrow-7\le x\le3\)

\(\Rightarrow x\in\left\{-7;-6;-5;-4;-3;....;2;3\right\}\)

-1/12<x<1/4

Do -1/12>-1

1/4<1

=>-1<-1/12<x<1/4<1(dòng này bỏ viết ra để hiểu thôi)

=>-1<x<1

Do x nguyên=>x=0

Đặt \(a=24-x,b=x-25\)

Khi đó pt ban đầu trở thành :

\(\frac{a^2+ab+b^2}{a^2-ab+b^2}=\frac{19}{49}\)

\(\Leftrightarrow49\left(a^2+ab+b^2\right)=19\left(a^2-ab+b^2\right)\)

\(\Leftrightarrow30a^2+68ab+30b^2=0\)

\(\Leftrightarrow15a^2+34ab+15b^2=0\)

\(\Leftrightarrow\left(3a+5b\right)\left(5a+3b\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3a=-5b\\5a=-3b\end{cases}}\)

Đến đây bạn thay vào là dễ rồi nhé ! Chúc bạn học tốt !

\(\Leftrightarrow\left(\dfrac{2}{3}x-1\right)^3\cdot\dfrac{1}{50}=\dfrac{75}{2}-24=\dfrac{27}{2}\)

\(\Leftrightarrow\left(\dfrac{2}{3}x-1\right)^3=\dfrac{27}{2}:\dfrac{1}{50}=675\)

\(\Leftrightarrow x\cdot\dfrac{2}{3}-1=3\sqrt[3]{25}\)

\(\Leftrightarrow x\cdot\dfrac{2}{3}=3\sqrt[3]{25}+1\)

\(\Leftrightarrow x=\dfrac{3\left(3\sqrt[3]{25}+1\right)}{2}\)