\(\dfrac{x+1}{99}+\dfrac{x+2}{98}+\dfrac{x+3}{97}+\dfrac{x+4}{96}=-4\)
⇔\(\dfrac{x+1}{99}+1+\dfrac{x+2}{98}+1+\dfrac{x+3}{97}+\dfrac{x+4}{96}=-4+1+1+1+1\)
⇔\(\dfrac{x+1}{99}+\dfrac{99}{99}+\dfrac{x+2}{98}+\dfrac{98}{98}+\dfrac{x+3}{97}+\dfrac{97}{97}+\dfrac{x+4}{96}+\dfrac{96}{96}=-4+4\)
⇔\(\dfrac{x+100}{99}+\dfrac{x+100}{98}+\dfrac{x+100}{97}+\dfrac{x+100}{96}=0\)
⇔\(\left(x+100\right)\left(\dfrac{1}{99}+\dfrac{1}{98}+\dfrac{1}{97}+\dfrac{1}{96}\right)=0\)
⇔\(x+100=0\left(\dfrac{1}{99}+\dfrac{1}{98}+\dfrac{1}{97}+\dfrac{1}{96}\ne0\right)\)
⇔\(x=-100\)
cíu được phần 1 thôi nhé
Bổ xung ý 2
\(\dfrac{1}{x}+\dfrac{y}{3}=\dfrac{5}{6}\\ \Rightarrow\dfrac{1}{x}=\dfrac{5}{6}-\dfrac{y}{3}\\ \Rightarrow\dfrac{1}{x}=\dfrac{5-2y}{6}\\ \Rightarrow x\cdot\left(5-2y\right)=6\)
`=>x;5-2y in Ư(6)={+-1;+-3;+-2;+-6}`
mà `5-2y` là số lẻ
nên `5-2y in {+-1;+-3}`
Ta có bảng sau :
| `5-2y` | `-1` | `-3` | `1` | `3` |
| `y` | `3(T//m)` | `4(T//m)` | `2(T//m)` | `1(T//m)` |
| `x` | `-1(L)` | `-3(L)` | `1(T//m)` | `3(T//m)` |
Vậy `x;y in {(1;2);(3;1)}`
