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\(\left(3x-\dfrac{1}{3}\right)^2=16=4^2\)
\(\Rightarrow\left[{}\begin{matrix}3x-\dfrac{1}{3}=4\\3x-\dfrac{1}{3}=-4\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}3x=4+\dfrac{1}{3}\\3x=-4+\dfrac{1}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}3x=\dfrac{13}{3}\\3x=-\dfrac{11}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{13}{9}\\x=-\dfrac{11}{9}\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Khó hiểu chút, bạn cố gắng:
Ta thấy: 1+2+3= \(\frac{3}{2}\).(1+3) ; 1+2+3+4=\(\frac{4}{2}.\left(1+4\right)\)...... ; tương tự ta được 1+2+3..+16=\(\frac{16}{2}.\left(1+16\right)\)
Từ trên suy ra: \(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16\left(1+2+...+16\right)}=1+\frac{1}{2}.3+\frac{1}{3}.\frac{3}{2}\left(1+2+3\right)+...+\frac{1}{16}.\frac{16}{2}.\left(1+2+...+16\right)\) \(=1+\frac{1}{2}.3+\frac{1}{2}.4+...+\frac{1}{2}.17=\frac{1}{2}.\left(3+4+...+17\right)\)
\(=1+\frac{1}{2}\left(3+4+...+17\right)=1+\frac{1}{2}.\frac{15}{2}.\left(3+17\right)\)
\(=1+75=76\)
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\(-\dfrac{3}{5}\times x+\dfrac{1}{2}=\dfrac{4}{5}\)
\(-\dfrac{3}{5}\times x=\dfrac{4}{5}-\dfrac{1}{2}\)
\(-\dfrac{3}{5}\times x=\dfrac{3}{10}\)
\(x=\dfrac{3}{10}:-\dfrac{3}{5}\)
\(x=-\dfrac{1}{2}\)
Vậy \(x=-\dfrac{1}{2}\)
\(\dfrac{1}{2}\times x+\dfrac{3}{8}=\dfrac{7}{16}\)
\(\dfrac{1}{2}\times x=\dfrac{7}{16}-\dfrac{3}{8}\)
\(\dfrac{1}{2}\times x=\dfrac{1}{16}\)
\(x=\dfrac{1}{8}\)
Vậy \(x=\dfrac{1}{8}\)
\(\dfrac{2}{3}x-\dfrac{5}{6}x=-\dfrac{1}{2}\)
\(x\times\left(\dfrac{2}{3}-\dfrac{5}{6}\right)=-\dfrac{1}{2}\)
\(x\times\dfrac{-1}{6}=-\dfrac{1}{2}\)
\(x=3\)
Vậy \(x=3\)
\(\dfrac{2}{5}x+\dfrac{3}{10}x=-\dfrac{1}{5}\)
\(x\times\left(\dfrac{2}{5}+\dfrac{3}{10}\right)=-\dfrac{1}{5}\)
\(x\times\dfrac{7}{10}=-\dfrac{1}{5}\)
\(x=-\dfrac{2}{7}\)
Vậy \(x=-\dfrac{2}{7}\).
![](https://rs.olm.vn/images/avt/0.png?1311)
Tìm số nguyên x, biết:
1) -16 + 23 + x = - 16
7+x=-16
x=-16-7
x=-23
2) 2x – 35 = 15
2x=15+35
2x=50
x=50:2
x=25
3) 3x + 17 = 12
3x=12-17
3x=-5
x=-5/3
4) (2x – 5) + 17 = 6
2x-5=6-17
2x-5=-11
2x=-11+5
2x=-6
x=-6:2
x=-3
5) 10 – 2(4 – 3x) = -4
2(4-3x)=10-(-4)
2(4-3x)=14
4-3x=14:2
4-3x=7
3x=4-7
3x=-3
x=-3:3
x=-1
6) - 12 + 3(-x + 7) = -18
3(-x+7)=-18-(-12)
3(x+7)=-6
x+7=-6:3
x+7=-2
x=-2-7
x=-9
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(3x-\dfrac{1}{3}\right)^2=16=4^2=\left(-4\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}3x-\dfrac{1}{3}=4\\3x-\dfrac{1}{3}=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=\dfrac{13}{3}\\3x=-\dfrac{11}{3}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{13}{9}\\x=-\dfrac{11}{9}\end{matrix}\right.\)