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$(1) binh phuong 2 ve\Leftrightarrow -2\sqrt{4x^{2}-y}=4x-y\Rightarrow 16x^{2}-4y=16x^{2}-8xy+y^{2}\Leftrightarrow y^{2}-8xy-4y=0\Rightarrow y=0(loai) \vee y-8x+4=0\Rightarrow y-6x=2x-4 thay vao (2)\Rightarrow \sqrt{4x^{2}-39}=3+\sqrt{2x-4} (x\geq \frac{\sqrt{39}}{2})\Leftrightarrow 2x^{2}-x-22-3\sqrt{2x-4}=0\Leftrightarrow 2(x-4)^{2}+15(x-4)-6.\frac{x-4}{\sqrt{2x-4}+2}\Rightarrow x=4, y=28(thoa DK) \vee 2x+7-\frac{6}{\sqrt{2x-4}+2}=0\Leftrightarrow 2x+4+\frac{\sqrt{2x-4}+6-6}{\sqrt{2x-4}+2}=0 vo ly vi pt >0 \forall x \geq \frac{\sqrt{39}}{2}$

bình phương 2 vế pt(1): $4x-2\sqrt{4x^{2}-y}=8x-y\Leftrightarrow 2\sqrt{4x^{2}-y}=y-4x\Rightarrow 4(4x^{2}-y)=16x^{2}-4xy+y^{2}\Leftrightarrow y^{2}-8xy+4y=0\Rightarrow y=0(loai) \vee y-8x+4=0\Leftrightarrow y-6x=2x-4 thay vao pt (2) \sqrt{4x^{2}-39}=3+\sqrt{2x-4}\Rightarrow 4x^{2}-39=9+6\sqrt{2x-4}+2x-4\Leftrightarrow 2x^{2}-x-22-3\sqrt{2x-4}=0\Leftrightarrow 2x^{2}-16x+32+15x-60+6-3\sqrt{2x-4}=0\Leftrightarrow 2(x-4)^{2}+15(x-4)-6.\frac{x-4}{\sqrt{2x-4}+2}=0\Rightarrow x=4 \vee 2x+7-\frac{6}{\sqrt{2x-4}+2}\Leftrightarrow 2x+4+\frac{3\sqrt{2x-4}+6-6}{\sqrt{2x-4}+2}=0\Leftrightarrow 2x+4+\frac{3\sqrt{2x-4}}{\sqrt{2x-4}+2}=0 vo ly do x\geq 2. vay voi x=4, y=28 thi thoa DK$

$ (1) binh phuong 2 ve\Leftrightarrow -2\sqrt{4x^{2}-y}=4x-y\Rightarrow 16x^{2}-4y=16x^{2}-8xy+y^{2}\Leftrightarrow y^{2}-8xy-4y=0\Rightarrow y=0(loai) \vee y-8x+4=0\Rightarrow y-6x=2x-4 thay vao (2)\Rightarrow \sqrt{4x^{2}-39}=3+\sqrt{2x-4} (x\geq \frac{\sqrt{39}}{2})\Leftrightarrow 2x^{2}-x-22-3\sqrt{2x-4}=0\Leftrightarrow 2(x-4)^{2}+15(x-4)-6.\frac{x-4}{\sqrt{2x-4}+2}\Rightarrow x=4, y=28(thoa DK) \vee 2x+7-\frac{6}{\sqrt{2x-4}+2}=0\Leftrightarrow 2x+4+\frac{\sqrt{2x-4}+6-6}{\sqrt{2x-4}+2}=0 vo ly vi pt >0 \forall x \geq \frac{\sqrt{39}}{2}$

$(1) binh phuong 2 ve\Leftrightarrow -2\sqrt{4x^{2}-y}=4x-y\Rightarrow 16x^{2}-4y=16x^{2}-8xy+y^{2}\Leftrightarrow y^{2}-8xy-4y=0\Rightarrow y=0(loai) \vee y-8x+4=0\Rightarrow y-6x=2x-4 thay vao (2)\Rightarrow \sqrt{4x^{2}-39}=3+\sqrt{2x-4} (x\geq \frac{\sqrt{39}}{2})\Leftrightarrow 2x^{2}-x-22-3\sqrt{2x-4}=0\Leftrightarrow 2(x-4)^{2}+15(x-4)-6.\frac{x-4}{\sqrt{2x-4}+2}\Rightarrow x=4, y=28(thoa DK) \vee 2x+7-\frac{6}{\sqrt{2x-4}+2}=0\Leftrightarrow 2x+4+\frac{\sqrt{2x-4}+6-6}{\sqrt{2x-4}+2}=0 vo ly vi pt >0 \forall x \geq \frac{\sqrt{39}}{2}$

$(1) binh phuong 2 ve\Leftrightarrow -2\sqrt{4x^{2}-y}=4x-y\Rightarrow 16x^{2}-4y=16x^{2}-8xy+y^{2}\Leftrightarrow y^{2}-8xy-4y=0\Rightarrow y=0(loai) \vee y-8x+4=0\Rightarrow y-6x=2x-4 thay vao (2)\Rightarrow \sqrt{4x^{2}-39}=3+\sqrt{2x-4} (x\geq \frac{\sqrt{39}}{2})\Leftrightarrow 2x^{2}-x-22-3\sqrt{2x-4}=0\Leftrightarrow 2(x-4)^{2}+15(x-4)-6.\frac{x-4}{\sqrt{2x-4}+2}\Rightarrow x=4, y=28(thoa DK) \vee 2x+7-\frac{6}{\sqrt{2x-4}+2}=0\Leftrightarrow 2x+4+\frac{\sqrt{2x-4}+6-6}{\sqrt{2x-4}+2}=0 vo ly vi pt >0 \forall x \geq \frac{\sqrt{39}}{2}$

$ (1) binh phuong 2 ve\Leftrightarrow -2\sqrt{4x^{2}-y}=4x-y\Rightarrow 16x^{2}-4y=16x^{2}-8xy+y^{2}\Leftrightarrow y^{2}-8xy-4y=0\Rightarrow y=0(loai) \vee y-8x+4=0\Rightarrow y-6x=2x-4 thay vao (2)\Rightarrow \sqrt{4x^{2}-39}=3+\sqrt{2x-4} (x\geq \frac{\sqrt{39}}{2})\Leftrightarrow 2x^{2}-x-22-3\sqrt{2x-4}=0\Leftrightarrow 2(x-4)^{2}+15(x-4)-6.\frac{x-4}{\sqrt{2x-4}+2}\Rightarrow x=4, y=28(thoa DK) \vee 2x+7-\frac{6}{\sqrt{2x-4}+2}=0\Leftrightarrow 2x+4+\frac{\sqrt{2x-4}+6-6}{\sqrt{2x-4}+2}=0 vo ly vi pt >0 \forall x \geq \frac{\sqrt{39}}{2}$

$\sqrt{2x+\sqrt{y}}-\sqrt{2x-\sqrt{y}}=\sqrt{8x-y}\Leftrightarrow -2\sqrt{4x^{2}-y}=4x-y\Rightarrow 16x^{2}-4y=16x^{2}-8xy+y^{2}\Leftrightarrow y^{2}-8xy-4y=0\Rightarrow y=0(loại) hoặc y-8x+4=0\Rightarrow y-6x=2x-4 thay vào (2)\Rightarrow \sqrt{4x^{2}-39}=3+\sqrt{2x-4} (x\geq \frac{\sqrt{39}}{2})\Leftrightarrow 2x^{2}-x-22-3\sqrt{2x-4}=0\Leftrightarrow 2(x-4)^{2}+15(x-4)-6.\frac{x-4}{\sqrt{2x-4}+2}\Rightarrow x=4, y=28(thoã đk) hoặc 2x+7-\frac{6}{\sqrt{2x-4}+2}=0\Leftrightarrow 2x+4+\frac{\sqrt{2x-4}+6-6}{\sqrt{2x-4}+2}>0$

$(1) binh phuong 2 ve\Leftrightarrow -2\sqrt{4x^{2}-y}=4x-y\Rightarrow 16x^{2}-4y=16x^{2}-8xy+y^{2}\Leftrightarrow y^{2}-8xy-4y=0\Rightarrow y=0(loai) \vee y-8x+4=0\Rightarrow y-6x=2x-4 thay vao (2)\Rightarrow \sqrt{4x^{2}-39}=3+\sqrt{2x-4} (x\geq \frac{\sqrt{39}}{2})\Leftrightarrow 2x^{2}-x-22-3\sqrt{2x-4}=0\Leftrightarrow 2(x-4)^{2}+15(x-4)-6.\frac{x-4}{\sqrt{2x-4}+2}\Rightarrow x=4, y=28(thoa DK) \vee 2x+7-\frac{6}{\sqrt{2x-4}+2}=0\Leftrightarrow 2x+4+\frac{\sqrt{2x-4}+6-6}{\sqrt{2x-4}+2}=0 vo ly vi pt >0 \forall x \geq \frac{\sqrt{39}}{2}$

$\sqrt{2x+\sqrt{y}}-\sqrt{2x-\sqrt{y}}=\sqrt{8x-y}\Leftrightarrow -2\sqrt{4x^{2}-y}=4x-y\Rightarrow 16x^{2}-4y=16x^{2}-8xy+y^{2}\Leftrightarrow y^{2}-8xy-4y=0\Rightarrow y=0(loại) hoặc y-8x+4=0\Rightarrow y-6x=2x-4 thay vào (2)\Rightarrow \sqrt{4x^{2}-39}=3+\sqrt{2x-4} (x\geq \frac{\sqrt{39}}{2})\Leftrightarrow 2x^{2}-x-22-3\sqrt{2x-4}=0\Leftrightarrow 2(x-4)^{2}+15(x-4)-6.\frac{x-4}{\sqrt{2x-4}+2}\Rightarrow x=4, y=28(thoã đk) hoặc 2x+7-\frac{6}{\sqrt{2x-4}+2}=0\Leftrightarrow 2x+4+\frac{\sqrt{2x-4}+6-6}{\sqrt{2x-4}+2}>0\forall x\geq \frac{\sqrt{39}}{2}$

$\sqrt{2x+\sqrt{y}}-\sqrt{2x-\sqrt{y}}=\sqrt{8x-y}\Leftrightarrow -2\sqrt{4x^{2}-y}=4x-y\Rightarrow 16x^{2}-4y=16x^{2}-8xy+y^{2}\Leftrightarrow y^{2}-8xy-4y=0\Rightarrow y=0(loại) hoặc y-8x+4=0\Rightarrow y-6x=2x-4 thay vào (2)\Rightarrow \sqrt{4x^{2}-39}=3+\sqrt{2x-4} (x\geq \frac{\sqrt{39}}{2})\Leftrightarrow 2x^{2}-x-22-3\sqrt{2x-4}=0\Leftrightarrow 2(x-4)^{2}+15(x-4)-6.\frac{x-4}{\sqrt{2x-4}+2}\Rightarrow x=4, y=28(thoã đk) hoặc 2x+7-\frac{6}{\sqrt{2x-4}+2}=0\Leftrightarrow 2x+4+\frac{\sqrt{2x-4}+6-6}{\sqrt{2x-4}+2}>0$