Question

tìm x

1/(x+2001) - 1/(x+2007) =7/8

Answer 1

\(\Leftrightarrow\frac{1}{x+2000}-\frac{1}{x+2007}=\frac{7}{\left(x+2000\right)\left(x+2007\right)}\)

\(\Rightarrow\frac{7}{\left(x+2000\right)\left(x+2007\right)}=\frac{7}{2^3}\)

\(\Rightarrow\frac{7\left(x^2+4007x+4013992\right)}{8\left(x+2000\right)\left(x+2007\right)}=0\)

áp dụng Delta ta có :

\(\Leftrightarrow x^2+4007x+4013992=0\)

\(\Rightarrow4007^2-4\left(1.4013992\right)=81\)

\(\Rightarrow x_{1,2}=\frac{-b+-\sqrt{D}}{2a}=\frac{-4007+-\sqrt{81}}{2}\)

=>x=-2008 hoặc -1999