\(\left(2x+1\right)\left(x+3\right)=2017\)
\(\Leftrightarrow2x\left(x+3\right)+\left(x+3\right)=2017\)
\(\Leftrightarrow2x^2+6x+x+3-2017=0\)
\(\Leftrightarrow2x^2+7x-2014=0\)
\(\Delta=7^2-\left[-4\cdot\left(2\cdot2014\right)\right]=16161\)
\(\Rightarrow x_{1,2}=\frac{-7\pm\sqrt{16161}}{4}\)
Ta có bảng sau:
2x+1 | 2017 | 1 | -2017 | -1 |
x+3 | 1 | 2017 | -1 | -2017 |
x | 1008 | 0 | -1009 | -1 |
x | -2 | 2014 | -4 | -2020 |
Vậy các cặp x thỏa mãn là: (1008;-2);(0;2014);(-1009;-4);(-1;-2020)