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lovelycat_handoi95

[tex]\left{x^3+y^3=1\\x^2y+2xy^2+y^3=2[/tex]

[tex]\Leftrightarrow \left{x^3+y^3=1\\ 2(x^3+y^3)-x^2y-2xy^2-y^3 =0 [/tex]

[tex]\Leftrightarrow \left{x^3+y^3=1\\ 2x(x^2-y^2)-y(x^2-y^2)=0 [/tex]

[tex]\Leftrightarrow \left{x^3+y^3=1\\ (x-y)(x+y)(2x-y)=0 [/tex]

[tex]TH1 : \left{x^3+y^3=1\\ x=y [/tex]

[tex]\Leftrightarrow x=y= \frac{1}{\sqrt[3]{2}}[/tex]

[tex]TH2: \left{x^3+y^3=1\\ x=-y [/tex]

[tex]\Rightarrow VN [/tex]

[tex]TH3 : \Leftrightarrow \left{x^3+y^3=1\\ y=2x [/tex]

[tex]\Leftrightarrow \left {x= \frac{\sqrt[3]{3}}{3} \\ y= \frac{2\sqrt[3]{3}}{3}[/tex]
 
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