Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Ta có: \(\left|4x-1\right|=\left|x+2\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}4x-1=x+2\\4x-1=-x-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=3\\5x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{5}\end{matrix}\right.\)
\(\frac{x}{1}\)= \(\frac{3}{x+2}\)
=> x (x+2) = 3
=> x+2 = 3
=> x = 1
Với mọi \(x\in R\)ta có:
\(\left|x\right|+\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|\ge0\Leftrightarrow6x\ge0\Leftrightarrow x\ge0\)
Với \(x\ge0\)thì: \(\left|x\right|=x;\left|x+1\right|=x+1;\left|x+2\right|=x+2;\left|x+3\right|=x+3;\left|x+4\right|=x+4\)
\(pt\Leftrightarrow5x+10=6x\Leftrightarrow x=10\)
a) \(5^{n+3}-5^{n+1}=5^{12}.120\Leftrightarrow5^{n+1}.\left(5^2-1\right)=5^{12}.5.24\)
\(\Leftrightarrow24.5^{n+1}=5^{13}.24\Leftrightarrow5^{n+1}=5^{13}\Leftrightarrow n+1=13\Leftrightarrow n=12\)
b) \(2^{n+1}+4.2^n=3.2^7\)
\(\Leftrightarrow2^n\left(2+4\right)=3.2^7\Leftrightarrow6.2^n=3.2^7\Leftrightarrow2^n=2^6\Leftrightarrow n=6\)
c) \(3^{n+2}-3^{n+1}=486\)
\(\Leftrightarrow3^{n+1}.\left(3-1\right)=486\Leftrightarrow2.3^{n+1}=486\Leftrightarrow3^{n+1}=243\)
\(\Leftrightarrow3^n=243:3=81=3^3\Leftrightarrow n=3\)
d) \(3^{2n+3}-3^{2n+2}=2.3^{10}\)
\(\Leftrightarrow3^{2n+2}.\left(3-1\right)=2.3^{10}\)
\(\Leftrightarrow3^{2n+2}.2=2.3^{10}\Leftrightarrow3^{2n+2}=3^{10}\Leftrightarrow2n+2=10\Leftrightarrow2n=8\Leftrightarrow n=4\)