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e,
\(2^x-15=17\\ 2^x=17+15\\ 2^x=32\\ 2^x=2^5\\ x=5\)
Vậy \(x=5\)
d,
\(\left(x-1\right)^5-\left(x-1\right)^2=0\\ \left(x-1\right)^2\cdot\left[\left(x-1\right)^3-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}\left(x-1\right)^2=0\\\left(x-1\right)^3-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x-1=0\\\left(x-1\right)^3=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\\left(x-1\right)^3=1^3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x-1=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
Vậy \(x=1\) hoặc \(x=2\)
mấy câu còn lại coi lại đề
PT <=> \(\frac{4x}{3}=\frac{14x}{3}+5\)
<=> \(\frac{10x}{3}=-5\)
<=> x= \(-5:\frac{10}{3}=-\frac{15}{10}=-\frac{3}{2}\)
vậy x= - 3/2
1,
để A thuộc Z thì
x+5 chia het cho x+3
co x+3 chia het cho x+3
=>(x+5)-(x+3)chia het cho x+3
hay2 chia het cho x+3
=>x+3 thuộc ước của 2
=>x+3 thuoc {1,-1,2,-2}
ta co bang
| x+3 | 1 | -1 | 2 | -2 |
| x | -2 | -4 | -1 | -5 |
vay de A thuoc Z thi x thuoc {-2,-4,-1,-2}
b,\(\Rightarrow\)\(\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}\right):2=\frac{2013}{2015}:2\)
\(\Rightarrow\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{2013}{4030}\)
\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{2013}{4030}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2013}{4030}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2013}{4030}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2015}\)
\(\Rightarrow\)\(x+1=2015\)
\(\Rightarrow x=2014\)
a, 2/3x -3/2.x-1/2x=5/12
x.(2/3-3/2-1/2)=5/12
x. -4/3=5/12
x=5/12:-4/3
x=-5/16
b,2/6+2/12+2/20+...+2/x.(x+1)=2013/2015
2/2.3+2/3.4+2/4.5+...+2/x.(x+1)=2013/2015
1/2(1-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1)=2013/2015
1/2(1-1/x+1)=2013/2015
1-1/x+1=2013/2015 : 1/2
1-1/x+1=4206/2015
suy ra đề sai
a/ \(\left|5x+\frac{3}{4}\right|-\frac{5}{4}=2\)
\(\left|5x+\frac{3}{4}\right|=\frac{13}{4}\)
- / \(5x+\frac{3}{4}=\frac{13}{4}\)
\(5x=\frac{5}{2}\)
\(x=\frac{1}{2}\) - / \(5x+\frac{3}{4}=-\frac{13}{4}\)
\(5x=-4\)
\(x=-\frac{4}{5}\)
\(\Rightarrow x=\left\{\frac{1}{2};-\frac{4}{5}\right\}\)
b/\(\frac{3}{2}-\left|\frac{1}{2}x+1\right|=\frac{1}{4}\)
\(\left|\frac{1}{2}x+1\right|=\frac{5}{4}\)
1/\(\frac{1}{2}x+1=\frac{5}{4}\)
\(\frac{1}{2}x=\frac{1}{4}\)
\(x=\frac{1}{2}\)
2/\(\frac{1}{2}x+1=-\frac{5}{4}\)
\(\frac{1}{2}x=-\frac{9}{4}\)
\(x=-\frac{9}{2}\)
\(\Rightarrow x=\left\{\frac{1}{2};-\frac{9}{2}\right\}\)
a) \(3x-\frac{3}{2}-5x+\frac{10}{3}=1\)
\(3x-5x=1+\frac{3}{2}-\frac{10}{3}\)
\(-2x=-\frac{5}{6}\)
\(x=\frac{5}{12}\)
b) \(\left|x-1\right|=5-x\)
Th1:
\(x-1=5-x\)
\(x+x=5+1\)
\(2x=6\)
\(x=3\)
Th2:
\(-\left(x-1\right)=5-x\)
\(x+1=5-x\)
\(x+x=5-1\)
\(2x=4\)
\(x=2\)
Vậy \(x=3\)và \(x=2\)
a) 3x - 5x = 1 + 3/2 - 10/3
-2x = -5/6
x = -5/6 : ( - 2 )
x = 5/12
b) |x-1|= 5-x
Nếu x \(\ge\)1 \(\Rightarrow\)x - 1 \(\ge\)0 \(\Rightarrow\)x - 1 = 5 - x.
2x = 6
x = 3.
Nếu x < 1 \(\Rightarrow\)x - 1 < 0 \(\Rightarrow\)Ix-1I = 1 - x
\(\Rightarrow\)1 - x = 5 - x \(\Rightarrow\)vô lý.
Vậy x = 3