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1/ a) \(x^2-x-1⋮x-1\)
=>\(x.\left(x-1\right)-1⋮x-1\)
=>\(-1⋮x-1\)(vì x.(x-1)\(⋮\)x-1)
=>x-1\(\inƯ\left(-1\right)\)
Đến đay tự làm
b/c/d/e/ tương tự
![](https://rs.olm.vn/images/avt/0.png?1311)
1/3+2/3x =1/4
=> 2/3x=1/4-1/3
=>2/3x=-1/12
=>x=-1/12:2/3
=>x=-1/8
:3
\(\frac{1}{3}+\frac{2}{3}x=\frac{1}{4}\)
1x=\(\frac{1}{4}\)
x=\(\frac{1}{4}\):1
vậy =1\(\frac{1}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) pt <=> \(\frac{x\left(x+1\right)}{2}=500500\)
<=> \(x^2+x=1001000\)
<=> \(x^2-1000x+1001x-1001000=0\)
<=> \(\left(x-1000\right)\left(x+1001\right)=0\)
<=> \(\orbr{\begin{cases}x=1000\\x=-1001\end{cases}}\)
Do \(x>0\)=> \(x=1000\)
b)
<=> \(2x=210\)
<=> \(x=105\)
c)
<=> \(6x-81=3.7\)
<=> \(x=17\)
d)
<=> \(125-5\left(3x-1\right)=5^2\)
<=> \(5\left(3x-1\right)=100\)
<=> \(3x-1=20\)
<=> \(x=7\)
e)
<=> \(4^{x+1}+1=65\)
<=> \(4^{x+1}=64\)
<=> \(x+1=3\)
<=> \(x=2\)
j)
<=> \(2\left(2x-3\right)=14\)
<=> \(2x-3=7\)
<=> \(x=5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,2x\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x\in\forall Z\\x=1\end{cases}}}\)
\(b,x\left(2x-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\2x-4=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}}\)
\(c;\left(x+1\right)+\left(x+3\right)+...............+\left(x+99\right)=0\)
\(\Rightarrow\left(x+x+...........+x\right)+\left(1+3+............+99\right)=0\)
\(\Rightarrow50x+2500=0\)
\(\Rightarrow50x=-2500\)
\(\Rightarrow x=-50\)
2/
\(a;\left(x-3\right)\left(2y+1\right)=7\)
\(\Rightarrow\left(x-3\right);\left(2y+1\right)\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
Xét bảng
x-3 | 1 | -1 | 7 | -7 |
2y+1 | 7 | -7 | 1 | -1 |
x | 4 | 2 | 10 | -4 |
y | 3 | -4 | 0 | -1 |
Vậy...............................
\(b;xy+3x-2y=11\)
\(\Rightarrow x\left(y+3\right)-2y-6=11-6\)
\(\Rightarrow x\left(y+3\right)-2\left(y+3\right)=5\)
\(\Rightarrow\left(x-2\right)\left(y+3\right)=5\)
\(\Rightarrow\left(x-2\right);\left(y+3\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)
Xét bảng'
x-2 | 1 | -1 | 5 | -5 |
y+3 | 5 | -5 | 1 | -1 |
x | 3 | 1 | 7 | -3 |
y | 2 | -8 | -2 | -4 |
Vậy................................
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\left|2x-5\right|+3\le17\)
\(\left|2x-5\right|\le17-3\)
\(\left|2x-5\right|\le14\)
\(\Rightarrow2x-5\le14\) hoặc \(2x-5\le-14\)
\(2x\le14+5\) hoặc \(2x\le-14+5\)
\(2x\le19\) hoặc \(2x\le-9\)
\(x\le19:2\) hoặc \(x\le-9:2\)
\(x\le9,5\)hoặc \(x\le-4,5\)
b) \(\left|5-3x\right|\ge4\)
\(\Rightarrow5-3x\ge4\) hoặc \(5-3x\ge-4\)
\(-3x\ge4-5\)hoặc \(-3x\ge-4-5\)
\(-3x\ge-1\) hoặc \(-3x\ge-9\)
\(x\le\frac{1}{3}\) hoặc \(x\le3\)
a)\(\frac{1}{3}+\frac{2}{3}x=\frac{1}{4}\)
\(\Rightarrow\frac{2}{3}x=\frac{1}{4}-\frac{1}{3}\)
\(\Rightarrow\frac{2}{3}x=-\frac{1}{12}\)
\(\Rightarrow x=-\frac{1}{12}:\frac{2}{3}\)
\(\Rightarrow x=-\frac{1}{8}\)
b)\(\left|3x+1\right|-17=-12\)
\(\Rightarrow\left|3x+1\right|=5\)
\(\Rightarrow\orbr{\begin{cases}3x+1=5\\3x+1=-5\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}3x=4\\3x=-6\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{4}{3}\\x=-2\end{cases}}\)
a, 1/3 \(+\)2/3 x \(=\)1/4
\(\Rightarrow\)2/3x \(=\)1/4 \(-\)1/3
\(\Rightarrow\)2/3 x \(=\)\(\frac{-1}{12}\)
\(\Rightarrow\)x \(=\)\(\frac{-1}{12}\)\(\div\)\(\frac{2}{3}\)
\(\Rightarrow\)x \(=\)\(\frac{-1}{12}\)\(\times\)\(\frac{2}{3}\)
\(\Rightarrow\)x \(=\)\(\frac{-1}{18}\)
b, \(|\)3x \(+\)1\(|\)\(-\)17 \(=\)-12
\(\Rightarrow\)\(|\)3x \(+\)1\(|\)\(=\)-12 \(+\)17
\(\Rightarrow\)\(|\)3x \(+\)1\(|\)\(=\)5
\(\Rightarrow\)3x \(+\)1 \(=\)5 ; 3x \(+\)1\(=\)-5
\(\Rightarrow\)3x \(=\)5 \(-\)1 ; 3x \(=\)-5 \(-\)1
\(\Rightarrow\)3x \(=\)4 ; 3x \(=\)-6
\(\Rightarrow\)x \(=\)4 : 3 ; x \(=\)-6 : 3
\(\Rightarrow\)x \(=\)\(\frac{4}{3}\); x \(=\)-2