Đk: \(x+4\ge0\Rightarrow x\ge-4\)

\(\left|2x+1\right|=x+4\)

\(\Rightarrow\left[\begin{matrix}2x-1=x+4\\2x-1=-x-4\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}2x-x=4+1\\2x+x=-4+1\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}x=5\left(tm\right)\\x=-1\left(loai\right)\end{matrix}\right.\)

Vậy x=5

TH1:x+y+z=0

\(\Rightarrow\left\{\begin{matrix}x+y=-z\\y+z=-x\\x+z=-y\end{matrix}\right.\)

\(\Rightarrow M=\frac{\left(x+y\right)\left(y+z\right)\left(z+x\right)}{8xyz}=\frac{-xyz}{8xyz}=\frac{-1}{8}\)

TH2: \(x+y+z\ne0\)

Ta có:

\(\frac{2x+2y-z}{z}=\frac{2x-y+2z}{y}=\frac{-x+2y+2z}{x}\)

\(\Rightarrow\left(\frac{2x+2y-z}{z}+3\right)=\left(\frac{2x-y+2z}{y}+3\right)=\left(\frac{-x+2y+2z}{x}+3\right)\)\(\Rightarrow\frac{2x+2y+z}{z}=\frac{2x+2y++2z}{y}=\frac{2x+2y+2z}{x}\)

\(\Rightarrow x=y=z\)

\(\Rightarrow M=\frac{\left(x+y\right)\left(y+z\right)\left(z+x\right)}{8xyz}=\frac{2x.2y.2z}{8xyz}=1\)

Vậy M=1 hoặc M=\(\frac{-1}{8}\)

Theo đề ra ta có: \(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}\)

Áp dụng tc dãy tỉ số bằng nhau ta có:
\(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}=\frac{a+b+c}{a+b+c}=1\)

\(\Rightarrow a=b=c\) (Đpcm)

bạn bấm vào đây !Cho x, y $\in$∈ Q. Chứng tỏ rằng:        a/ | x + y | $\le$≤ | x | + | y |              b/ | x - y | $\ge$≥ | x | - | y | 

\(2008-\left|2x-2008\right|=2x\)

\(\Rightarrow\left|2x-2008\right|=-\left(2x-2008\right)\)

Ta có: \(-\left(2x-2008\right)\le0\Rightarrow2x-2008\ge0\Rightarrow2x\ge2008\Rightarrow x\ge1004\)Vậy \(x\ge1004\)

\(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)

\(\)\(\Rightarrow\left(x-7\right)^{x+1}.\left[1-\left(x-7\right)^{10}\right]=0\)

\(\Rightarrow\left[\begin{matrix}\left(x-7\right)^{x+1}=0\\1-\left(x-7\right)^{10}=0\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}x-7=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}x-7=0\\\left[\begin{matrix}x-7=1\\x-7=-1\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}x=7\\\left[\begin{matrix}x=8\\x=6\end{matrix}\right.\end{matrix}\right.\)

Vậy....

Các số nguyên tố có 1 chữ số là 2,3,5,7