ĐK:x≥0
PT(1)⇔√x(2x−y)+y(2x−y)=0⇔(2x−y)(√x+y)=0
⇔y=2x⊻
+)Với y=2x pt (2)
\Leftrightarrow 2x(\sqrt{x^2+1}-1)=\sqrt{3x^2+3}
\Leftrightarrow 2x(\sqrt{x^2+1}-2)+2x-\sqrt{3x^2+3}=0
\Leftrightarrow \frac{2x(x^2-3)}{\sqrt{x^2+1}+2}+\frac{x^2-3}{2x+\sqrt{3x^2+3}}=0
\Leftrightarrow (x^2-3)(\frac{2x}{\sqrt{x^2+1}+2}+\frac{1}{2x+\sqrt{3x^2+3}})=0
\Leftrightarrow x^2-3=0
\Leftrightarrow x=\sqrt{3}
+) Với y=-\sqrt{x} pt (2)
\Leftrightarrow -\sqrt{x}(\sqrt{x^2+1}-1)=\sqrt{3x^3+3} ( vô nghiệm)
Vậy ..........
~~~~Amen~~~~