pt(1)
\Leftrightarrow\frac{6x}{y}-2-
\sqrt{3x-y}-3y=0
\Leftrightarrow\frac{2(3x-y)}{y^{2}}-\frac{\sqrt{3x-y}}{y}-3=0
Đặt t=\frac{\sqrt{3x-y}}{y}\Rightarrow2t^{2}-t-3=0\Rightarrowt=\frac{3}{2} or t=-1
TH1:t=\frac{3}{2}\Rightarrow\frac{\sqrt{3x-y}}{y}=\frac{3}{2}\Rightarrow\sqrt{3x-y}=\frac{3}{2}y(y\geq0)(1)
Thế(1) vào pt(2) ta đc:2\sqrt{3x+\frac{3}{2}y}=6x+3y-4\Leftrightarrow6x+3y-\sqrt{2}.\sqrt{6x+3y}-4=0
Đặt u=\sqrt{6x+3y}(u\geq0)\Rightarrowu=2\sqrt{2}(t/m) or u=-\sqrt{2}(L)
\Rightarrow\sqrt{6x+3y}=2\sqrt{2}(2)
Kết hợp (1)&(2)\Rightarrow(x;y)=(\frac{8}{9};\frac{8}{9})
TH2:t=-1.
Làm tương tự:\Rightarrow(x;y)=...