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[thao phuong]

Cho x,y thỏa $x^{2} + y^{2}= xy-x+2y$ . Chứng minh rằng $\frac{-2\sqrt{3}}{3}\leqslant x\leq \frac{2\sqrt{3}}{3}$

[dogsteven]

$y^2-(x+2)y+x^2+x=0$ có $\Delta = (x+2)^2-4(x^2+x)=-3x^2+4\geqslant 0$