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a)\(\left(\frac{4}{5}\right)^{2x+7}=\left(\frac{4}{5}\right)^4\)
=> 2x + 7 = 4
2x = 4 - 7
2x = -3
x = -3 : 2
x = -1,5
Vậy x = -1,5
a) nếu x-1 >= 0 hay x >=1 ta có |x-1|=x-1
nếu x-1 < 0 hay x < 1 ta có |x-1| = 1-x
với x >= 1 ta có
|x-1| = 2x - 5
x-1 = 2x - 5
x-2x = -5 + 1
-x = -4
x=4 ( thỏa mãn khoảng xét x>=1)
với x < 1 ta có
|x-1| = 2x - 5
1-x = 2x - 5
-x - 2x = -5 -1
-3x = -6
x=2 ( không thỏa mãn khoảng xét x < 1 )
\(\left(2x+1\right)^4=\left(2x+1\right)^6\)
\(\Rightarrow\left(2x+1\right)^6-\left(2x+1\right)^4=0\)
\(\Rightarrow\left(2x+1\right)^4.\left[\left(2x+1\right)^2-1\right]=0\)
\(\Rightarrow\left(2x+1\right)^4=0\) hoặc \(\left(2x+1\right)^2-1=0\)
+) \(\left(2x+1\right)^4=0\Rightarrow2x+1=0\Rightarrow x=-0,5\)
+) \(\left(2x+1\right)^2-1=0\Rightarrow\left(2x+1\right)^2=1\)
\(\Rightarrow2x+1=\pm1\)
+ \(2x+1=1\Rightarrow x=0\)
+ \(2x+1=-1\Rightarrow x=-1\)
Vậy \(x\in\left\{-0,5;0;-1\right\}\)
(2x+1)4=(2x+1)6
\(\Leftrightarrow\)16x+1=64x+1
\(\Leftrightarrow\)16x-64x=1-1
\(\Leftrightarrow\)-48x=0
\(\Leftrightarrow\)x=0
mik ko chắc..
Ta có:
\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{x\left(x+3\right)}=\frac{101}{1540}\)
\(\Rightarrow\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{101}{1540}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x+3}=\frac{101}{1540}.3=\frac{303}{1540}\)
\(\Rightarrow\frac{1}{x+3}=\frac{1}{5}-\frac{303}{1540}=\frac{1}{308}\)
\(\Rightarrow x+3=308\Leftrightarrow x=305\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|\dfrac{1}{2}x-\dfrac{1}{4}\right|-3=-4\\\left|\dfrac{1}{2}x-\dfrac{1}{4}\right|-3=4\end{matrix}\right.\Leftrightarrow\left|\dfrac{1}{2}x-\dfrac{1}{4}\right|=7\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x-\dfrac{1}{4}=7\\\dfrac{1}{2}x-\dfrac{1}{4}=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x=\dfrac{29}{4}\\\dfrac{1}{2}x=-\dfrac{27}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{29}{2}\\x=-\dfrac{27}{2}\end{matrix}\right.\)
\(\left|x+\dfrac{1}{2}\right|+\left|x+\dfrac{1}{3}\right|+\left|x+\dfrac{1}{4}\right|=4x\)
Mà \(\left\{{}\begin{matrix}\left|x+\dfrac{1}{2}\right|\ge0\\\left|x+\dfrac{1}{3}\right|\ge0\\\left|x+\dfrac{1}{4}\right|\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left|x+\dfrac{1}{2}\right|+\left|x+\dfrac{1}{3}\right|+\left|x+\dfrac{1}{4}\right|\ge0\)
\(\Leftrightarrow4x\ge0\)
\(\Leftrightarrow x+\dfrac{1}{2}+x+\dfrac{1}{3}+x+\dfrac{1}{4}=4x\)
\(\Leftrightarrow3x+1=4x\)
\(\Leftrightarrow x=1\left(tm\right)\)
Vậy ..
\(\dfrac{x-1}{2016}+\dfrac{x-2}{2015}+\dfrac{x-3}{2014}=3\)
\(\Rightarrow\left(\dfrac{x-1}{2016}-1\right)+\left(\dfrac{x-2}{2015}-1\right)+\left(\dfrac{x-3}{2014}-1\right)=0\)
\(\Rightarrow\dfrac{x-2017}{2016}+\dfrac{x-2017}{2015}+\dfrac{x-2017}{2014}=0\)
\(\Rightarrow\left(x-2017\right)\left(\dfrac{1}{2016}+\dfrac{1}{2015}+\dfrac{1}{2014}\right)=0\)
Vì \(\dfrac{1}{2016}+\dfrac{1}{2015}+\dfrac{1}{2014}\ne0\) nên \(x-2017=0\Leftrightarrow x=2017\)
\(\left|\left|2\text{x}-1\right|-3\right|=1\)
*TH1 :
=> |2x-1| - 3 = 1
=> | 2x-1 | = 4
+Th1 :
2x-1 = 4
=> 2x = 5
=> x= \(\dfrac{5}{2}\)
+Th2 :
2x - 1 = -4
=> 2x = -3
=> x= \(\dfrac{-3}{2}\)
*TH2 :
| 2x-1 | - 3 = -1
=> | 2x - 1 | = 2
+Th1 :
2x- 1 = 2
=> 2x = 3
=> x = \(\dfrac{3}{2}\)
+Th2 :
2x - 1 = -2
=> 2x = -1
=> x = \(\dfrac{-1}{2}\)
Vậy : x = \(\dfrac{-1}{2}\) hoặc x = \(\dfrac{5}{2}\) hoặc x= \(\dfrac{3}{2}\) hoặc x = \(\dfrac{-3}{2}\)