Ta có: [tex]x^{4}+x^{2}y^{4}+y^{6}=y^{4}+x^{6}+x^{4}y^{2} \Leftrightarrow x^4-y^4+x^2y^4-x^4y^2+y^6-x^6=0\Leftrightarrow -(x^2-y^2)(x^2+y^2)(x^2+y^2-1)=0\Rightarrow x^2=y^2 hoặc x^2+y^2=1[/tex]
+ [tex]x^2=y^2\Rightarrow x^8=y^8\Rightarrow x^8+y^8=2x^8=1\Rightarrow x^8=\frac{1}{2}\Rightarrow x=\pm \frac{1}{\sqrt[8]{2}}\Rightarrow (x,y)=(\frac{1}{\sqrt[8]{2}};\frac{1}{\sqrt[8]{2}});(\frac{1}{\sqrt[8]{2}};-\frac{1}{\sqrt[8]{2}});(-\frac{1}{\sqrt[8]{2}};-\frac{1}{\sqrt[8]{2}}) và hoán vị[/tex]
+ [tex]x^2+y^2=1\Rightarrow x^2=1-y^2\Rightarrow x^8=(1-y^2)^4=1-y^8\Rightarrow 1-4y^6+6y^4-4y^2+y^8=1-y^8\Rightarrow 2y^8-4y^6+6y^4-4y^2=0\Rightarrow 2y^2(y^6-2y^4+3y^2-2)=0\Rightarrow 2y^2(y^2-1)(y^4-y^2+2)=0\Rightarrow y=0 hoặc y=\pm 1[/tex]
* [tex]y=0\Rightarrow y=\pm 1[/tex]
* [tex]y=\pm 1\Rightarrow x=0[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
