tìm x,y biết (x-2).(5-x)=|2y+1|+2

`(x-2).(5-x)=|2y+1|+2`

`<=>|2y+1|+2 ≥0=>(x-2).(5-x) ≥0`

`<=>` \(\left[ \begin{array}{l}x-2<0\\x-2>0\end{array} \right.\) $↔️\left[ \begin{array}{l}5-x<0\\5-x>0\end{array} \right.$

`<=>` \(\left[ \begin{array}{l}x>2\\x<5\end{array} \right.\) 

`<=>2<x<5=>` \(\left[ \begin{array}{l}x=3\\x=4\end{array} \right.\) 

 `TH_1` : Nếu `x=4`

\(\left[ \begin{array}{l}2=|2y+1|+2\\y=-\dfrac{1}{2}\end{array} \right.\) 

`TH_2` : Nếu `x=3`

\(\left[ \begin{array}{l}(x-2).(5-x)=|2y+1|+2\\y=-\dfrac{1}{2}\end{array} \right.\) 

Vậy `(x;y)(x;y)=(4;-1/2)(3;-1/2)`

Hay \(\left[ \begin{array}{l}y=4\\x=-\dfrac{1}{2}\end{array} \right.\) ; \(\left[ \begin{array}{l}x=3\\y=-\dfrac{1}{2}\end{array} \right.\)