\(\dfrac{100}{x}-\dfrac{100}{x+2}=\dfrac{5}{6}\)ĐK : \(x\ne0;-2\)
\(\Leftrightarrow\dfrac{600\left(x+2\right)-600x}{6x\left(x+2\right)}=\dfrac{5x\left(x+2\right)}{6x\left(x+2\right)}\)
\(\Rightarrow1200=5x^2+10x\Leftrightarrow5x^2+10x-1200=0\)
\(\Leftrightarrow x=-1\pm\sqrt{241}\)( theo delta )
Vậy tập nghiệm của pt là S = { ... }
\(\dfrac{100}{x}-\dfrac{100}{x+2}=\dfrac{5}{6}\)
\(\Rightarrow600\left(x+2\right)-600x=5x\left(x+2\right)\)
\(\Rightarrow600x+1200-600x=5x^2+10x\)
\(\Rightarrow5x^2+10x-1200=0\)
\(\Rightarrow\Delta=b^2-4ac=10^2-4.-1200.5=24100\)
\(\Rightarrow\sqrt{\Delta}=\sqrt{24100}=10\sqrt{241}\)
\(\Rightarrow\left\{{}\begin{matrix}x_1=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-10+10\sqrt{241}}{2.5}=-1+\sqrt{241}\\x_2=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-10-10\sqrt{241}}{2.5}=-1-\sqrt{241}\end{matrix}\right.\)
