Bài 1:
a/ \(\Leftrightarrow\left(\left[x\right]-1\right)\left(\left[x\right]-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[x\right]=1\\\left[x\right]=4\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}1\le x< 2\\4\le x< 5\end{matrix}\right.\)
b/ \(\Leftrightarrow\left(\left[x\right]-2\right)\left(\left[x\right]-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[x\right]=2\\\left[x\right]=4\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}2\le x< 3\\4\le x< 5\end{matrix}\right.\)
Bài 2:
\(\Leftrightarrow2\left[x\right]=\left[x\right]+\left\{x\right\}+2\left\{x\right\}\)
\(\Leftrightarrow\left[x\right]=3\left\{x\right\}\)
\(\Rightarrow0\le\left[x\right]< 3\)
- Với \(\left[x\right]=0\Rightarrow\left\{x\right\}=0\Rightarrow x=0\)
- Với \(\left[x\right]=1\Rightarrow\left\{x\right\}=\frac{1}{3}\Rightarrow x=\frac{4}{3}\)
- Với \(\left[x\right]=2\) \(\Rightarrow\left\{x\right\}=\frac{2}{3}\Rightarrow x=\frac{8}{3}\)
Bài 3:
\(A>\frac{a}{a+b+c+d}+\frac{b}{a+b+c+d}+\frac{c}{a+b+c+d}+\frac{d}{a+b+c+d}=1\)
\(A< \frac{2a}{a+b+c+d}+\frac{2b}{a+b+c+d}+\frac{2c}{a+b+c+d}+\frac{2d}{a+b+c+d}=2\)
\(\Rightarrow1< A< 2\Rightarrow\left[A\right]=1\)
