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PT(1): $2xy-x+4y=(2y+1)\sqrt{x^2+2y}$
$\Leftrightarrow (2y+1)(-\sqrt{x^2+2y}+x+1)+2y-2x-1=0$
$\Leftrightarrow (2x-2y+1)(\frac{2y+1}{x+1+\sqrt{x^2+2y}}-1)=0$
$\Leftrightarrow (2x-2y+1)(2y-x-\sqrt{x^2+2y})=0$
$\Leftrightarrow (2x-2y+1).\frac{2y(2y-2x-1)}{2y-x+\sqrt{x^2+2y}}=0$
$\Leftrightarrow 2x-2y+1=0$ (do ĐKXĐ nên y>0)
Thay PT(2):
$3x-2=\sqrt{4x-1}+\sqrt{3x^2+2x-1}\geq 0$
$\Leftrightarrow (x-1-\sqrt{4x-1})+(2x-1-\sqrt{3x^2+2x-1})=0$
$\Leftrightarrow (x^2-6x+2).\frac{3x-2+\sqrt{4x-1}+\sqrt{3x^2+2x-1}}{(x-1-\sqrt{4x-1})(2x-1-\sqrt{3x^2+2x-1})}=0$
$\Leftrightarrow x^2-6x+2=0$
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