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Một số bài tập:$1).\left\{ \begin{array}{l} x^3-3x^2-9x+22=y^3+3y^2-9y\\ x^2+y^2-x+y=\frac{1}{2} \end{array} \right.$$2.)\left\{ \begin{array}{l} x+y-\sqrt{xy}=3\\ \sqrt{x+1}+\sqrt{y+1}=4 \end{array} \right.$$3.)\left\{ \begin{array}{l} x^4+y^2-xy^3-\frac{9}{8}x=0\\ y^4+x^2-yx^3-\frac{9}{8}y=0 \end{array} \right.$$4.)\left\{ \begin{array}{l} 4\sqrt{1+\frac{1}{x^2}+\frac{1}{(x+1)^2}}+5y=(\sqrt{y}+2\sqrt{y+1})^2\\ 4\sqrt{1+\frac{1}{y^2}+\frac{1}{(y+1)^2}}+5x=(\sqrt{x}+2\sqrt{x+1})^2 \end{array} \right.$$5).\left\{ \begin{array}{l} (x+y)(3xy-4\sqrt{x})=-2\\ (x+y)(3xy-4\sqrt{y})=2 \end{array} \right.$

Một số bài tập:$1).\left\{ \begin{array}{l} x^3-3x^2-9x+22=y^3+3y^2-9y\\ x^2+y^2-x+y=\frac{1}{2} \end{array} \right.$ HD : Đạo hàm pt (1)$2.)\left\{ \begin{array}{l} x+y-\sqrt{xy}=3\\ \sqrt{x+1}+\sqrt{y+1}=4 \end{array} \right.$ ( ĐH KA -2005)$3.)\left\{ \begin{array}{l} x^4+y^2-xy^3-\frac{9}{8}x=0\\ y^4+x^2-yx^3-\frac{9}{8}y=0 \end{array} \right.$$4.)\left\{ \begin{array}{l} 4\sqrt{1+\frac{1}{x^2}+\frac{1}{(x+1)^2}}+5y=(\sqrt{y}+2\sqrt{y+1})^2\\ 4\sqrt{1+\frac{1}{y^2}+\frac{1}{(y+1)^2}}+5x=(\sqrt{x}+2\sqrt{x+1})^2 \end{array} \right.$$5).\left\{ \begin{array}{l} (x+y)(3xy-4\sqrt{x})=-2\\ (x+y)(3xy-4\sqrt{y})=2 \end{array} \right.$