100/x-100/x+10=1/2 lưu ý là 100 trên x và 100 trên x+10 nha

Đáp án:

 $\dfrac{100}{x}-\dfrac{100}{x+10}=\dfrac{1}{2}$ $\text{(x $\neq$ 0;-10)}$

$⇔100.(\dfrac{1}{x}-\dfrac{1}{x+10})=\dfrac{1}{2}$

$⇔ \dfrac{1.(x+10)}{x.(x+10)}-\dfrac{x}{x.(x+10)}= \dfrac{1}{2}:100$

$⇒ \dfrac{x+10-x}{x.(x+10)}=\dfrac{1}{200}$

$⇔ \dfrac{10}{x.(x+10)}= \dfrac{0,005x.(x+10)}{x.(x+10)}$

$⇒ 10= 0,005x^2+\dfrac{1}{20}x$

$⇔ 10-\dfrac{1}{200}x^2-\dfrac{1}{20}x=0$ 

$⇔ \dfrac{2000}{200}-\dfrac{1x^2}{200}-\dfrac{10x}{200}=\dfrac{0}{200}$

$⇔ 2000-x^2-10x=0$

$⇔ -x^2-10x+2000=0$

$⇔ -(x^2+10x-2000)=0$

$⇔ -(x^2+50x-40x-2000)=0$

$⇔ -[x.(x+50)-40.(x+50)]=0$

$⇔ -(x-40).(x+50)=0$

$⇔$\(\left[ \begin{array}{l}-x+40=0\\x+50=0\end{array} \right.\) $⇔$ \(\left[ \begin{array}{l}-x=-40\\x=-50\end{array} \right.\) $⇔$ \(\left[ \begin{array}{l}x=40(tm)\\x=-50(tm)\end{array} \right.\) 

$\text{Vậy S={40;-50}}$