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\(1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+...+\frac{1}{x}.\left(1+2+3+...+x\right)=115\)
\(\Rightarrow1.\left(\frac{1.2}{2}\right)+\frac{1}{2}.\left(\frac{2.3}{2}\right)+\frac{1}{3}.\left(\frac{3.4}{2}\right)+....+\frac{1}{x}.\left[\frac{x\left(x+1\right)}{2}\right]=115\)
\(\Rightarrow\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+....+\frac{x+1}{2}=115\Rightarrow2+3+...+\left(x+1\right)=230\)
\(\frac{\Rightarrow\left[\frac{\left(x+1-2\right)}{1}+1\right].\left(x+1+2\right)}{2}=\frac{x.\left(x+3\right)}{2}=230\Rightarrow x.\left(x+3\right)=460\)
vì x và x+3 là 2 số tự nhiên cách nhau 3 đơn vị => \(x.\left(x+3\right)=460=20.23\Rightarrow x=20\)
Vậy x=20
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(\frac{4}{3}-\left(x-\frac{1}{5}\right)=\left|\frac{-3}{10}+\frac{1}{2}\right|-\frac{1}{6}\)
\(\frac{4}{3}-\left(x-\frac{1}{5}\right)=\frac{1}{5}-\frac{1}{6}\)
\(\frac{4}{3}-\left(x-\frac{1}{5}\right)=\frac{1}{30}\)
\(x-\frac{1}{5}=\frac{4}{3}-\frac{1}{30}\)
\(x-\frac{1}{5}=\frac{13}{10}\)
\(x=\frac{13}{10}+\frac{1}{5}\)
\(x=\frac{3}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
2/3-1/3(x-3/2)-1/2(2x+1)=5
2/3-1/3x-1/3.(-3/2)-1/2.2x-1/2.1=5
2/3-1/3x+1/2-x-1/2=5
-1/3x-x+2/3+1/2-1/2=5
-4/3x+2/3=5
-4/3x=5-2/3
-4/3x=13/3
=>x=13/3:(-4/3)
x=-13/4
![](https://rs.olm.vn/images/avt/0.png?1311)
mặc kệ biến chú tâm vào hệ trong ngoặc rồi mũ nó lên
a)1
b)1