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Giải hệ phương trình:
1, \(\left\{{}\begin{matrix}x^2+1+y^2+xy=y\\x+y-2=\frac{y}{1+x^2}\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^3+8y^3-4xy^2=1\\2x^4+8y^4-2x-y=0\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}x^2+y^2=\frac{1}{5}\\4x^2+3x-\frac{57}{25}=-y\left(3x+1\right)\end{matrix}\right.\)
4, \(\left\{{}\begin{matrix}\sqrt{12-y}+\sqrt{y\left(12-x\right)}=12\\x^3-8x-1=2\sqrt{y-2}\end{matrix}\right.\)
5, \(\left\{{}\begin{matrix}\left(1-y\right)\sqrt{x-y}+x=2+\left(x-y-1\right)\sqrt{y}\\2y^2-3x+6y+1=2\sqrt{x-2y}-\sqrt{4x-5y-3}\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\sqrt{y^2-7x-6}-\sqrt[3]{y\left(x-6\right)}=1\\\sqrt{2\left(x-y\right)^2+6x-2y+4}-\sqrt{y}=\sqrt{x+1}\end{matrix}\right.\)
a)\(\left\{{}\begin{matrix}2x+\left|y\right|=3\\x-y=6\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}\sqrt{3}x+y=\sqrt{2}\\\sqrt{3}x-\sqrt{2}y=-1\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}2\sqrt{x+3}+\sqrt{y^2-4y+4}=2\\\sqrt{x+3}-3\left|2-y\right|=1\end{matrix}\right.\)
Giải hệ phương trình:
a)\(\left\{{}\begin{matrix}x+y-\sqrt{xy}=3\\\sqrt{x+1}+\sqrt{y+1}=4\end{matrix}\right.\) \(\left(x,y\in R\right)\)
b) \(\left\{{}\begin{matrix}\sqrt{x}+\sqrt[4]{32-x}=y^2-3\\\sqrt[4]{x}+\sqrt{32-x}=24-6y\end{matrix}\right.\)
a)\(\left\{{}\begin{matrix}\sqrt{2}x-\sqrt{3}y=1\\x+\sqrt{3}y=\sqrt{2}\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}x-2\sqrt{2}y=\sqrt{5}\\\sqrt{2}x+y=1-\sqrt{10}\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}\left(\sqrt{2}-1\right)x-y=\sqrt{2}\\x+\left(\sqrt{2}+1\right)y=1\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}\sqrt{3}x-\sqrt{2}y=1\\\sqrt{2}x+\sqrt{3}y=\sqrt{3}\end{matrix}\right.\)
Giải hệ phương trình
a. \(\left\{{}\begin{matrix}\left(2-\sqrt{3}\right)x-3y=2+5+\sqrt{3}\\4x+y=4-2\sqrt{x}\end{matrix}\right.\)
b. \(\left\{{}\begin{matrix}x\sqrt{2}-y\sqrt{3}=1\\x+y\sqrt{3}=2\end{matrix}\right.\)
Cho biểu thức P=\(\left(\dfrac{2\sqrt{x}+x}{x\sqrt{x}-1}-\dfrac{1}{\sqrt{x}-1}\right):\left(1-\dfrac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\)
a, Rút gọn P.
b,Tính \(\sqrt{P}\) khi x=5 +2\(\sqrt{3}\)
Giải hệ phương trình: \(\left\{{}\begin{matrix}\left|x+5\right|-\frac{2}{\sqrt{y}-2}=4\\\left|x+5\right|+\frac{1}{\sqrt{y}-2}=3\end{matrix}\right.\)
Giải hệ phương trình sau: \(\left\{{}\begin{matrix}\sqrt{3+2x^2y-x^4y^2}+x^2\left(1-2x^2\right)=y^4\\1+\sqrt{1+\left(x-y\right)^2}+x^2\left(x^4-2x^2-2xy^2+1\right)=0\end{matrix}\right.\)
