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a) \(\left[\left(x+32\right)-17\right].2=42\)
\(\left[\left(x+32\right)-17\right]=42:2\)
\(\left[\left(x+32\right)-17\right]=21\)
\(\left(x+32\right)=21+17\)
\(\left(x+32\right)=38\)
\(x=38-32\)
\(x=6\)
b) \(125+\left(145-x\right)=175\)
\(\left(145-x\right)=175-125\)
\(\left(145-x\right)=50\)
\(x=145-50\)
\(x=95\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: x(1+30%)=-1,31
⇒ \(\dfrac{13}{10}\)x =-1,31
⇒ x =-1,31 : \(\dfrac{13}{10}\)
⇒ x = -\(\dfrac{131}{130}\)
x + 30% x = -1,31
\(x+\dfrac{30}{100}x=-1,31\)
x+0,3x=-1,31
x.(0,3+1)=-1,31
x.1,3=-1,31
\(x=\dfrac{-1,31}{1,3}\)
\(x=-\dfrac{131}{130}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow x-\left[3-x+3+x-2\right]=0\)
=>x=4
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^{15}=x\)
\(\Rightarrow x^{15}-x=0\)
\(\Rightarrow x.\left(x^{14}-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x^{14}-1=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x^{14}=0+1=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
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1.
a.
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}=1-\frac{1}{6}=\frac{5}{6}\)
b.
Tích có 100 thừa số
=> n = 100
\(\left(100-1\right)\times\left(100-2\right)\times\left(100-3\right)\times...\times\left(100-99\right)\times\left(100-100\right)\)
\(=\left(100-1\right)\times\left(100-2\right)\times\left(100-3\right)\times...\times\left(100-99\right)\times0\)
\(=0\)
2.
a.
\(135\times789789-789\times135135=1001\times\left(135\times789-789\times135\right)=1001\times0=0\)
b.
\(\left(28\times9696-96\times2828\right)\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=\left[101\times\left(28\times96-96\times28\right)\right]\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=\left(101\times0\right)\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=0\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=0\)
3.
a.
\(\left[\left(x+32\right)-17\right]\times2=42\)
\(\left(x+32\right)-17=\frac{42}{2}\)
\(\left(x+32\right)-17=21\)
\(x+32=21+17\)
\(x+32=38\)
\(x=38-32\)
\(x=6\)
b.
\(125+\left(145-x\right)=175\)
\(145-x=175-125\)
\(145-x=50\)
\(x=145-50\)
\(x=95\)
x + 175 và x + 125 đều là bội của x
\(\Rightarrow\) 175; 125 \(\in\) B(x)
\(\Rightarrow x\inƯC\left(175;125\right)\)
175 = 52.7
125 = 53
\(\Rightarrow\) ƯCLN(175;125) = 52 = 25
\(\Rightarrow\) x \(\in\) Ư(25) = {1;5;25}