Đáp án: $(x,y)= (\dfrac{140}{17},\dfrac{140}{31})$
Giải thích các bước giải:
Ta có:
$35(x+y)=120(x-y)$
$\to 35x+35y=120x-120y$
$\to 155y=85x$
$\to y=\dfrac{17}{31}x$
Mà $35(x+y)=12xy$
$\to 35(x+\dfrac{17}{31}x)=12x\cdot \dfrac{17}{31}x$
$\to 35\cdot \dfrac{48}{31}x=\dfrac{204}{31}x^2$
$\to \dfrac{1680}{31}x=\dfrac{204}{31}x^2$
$\to \dfrac{204}{31}x^2-\dfrac{1680}{31}x=0$
$\to x(\dfrac{204}{31}x-\dfrac{1680}{31})=0$
$\to x=0\to y=0$
Hoặc $\dfrac{204}{31}x-\dfrac{1680}{31}=0\to x=\dfrac{140}{17}$
$\to y=\dfrac{17}{31}\cdot \dfrac{140}{17}=\dfrac{140}{31}$
$\to (x,y)\in\{(0,0), (\dfrac{140}{17},\dfrac{140}{31})\}$
Mà $x,y>0\to (x,y)= (\dfrac{140}{17},\dfrac{140}{31})$
