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Bình phương 2 vế pt đầu:
\(4x^2+y^2+4x+1+2\sqrt{\left(4x^2+y^2\right)\left(4x+1\right)}=4y-4\)
\(\Leftrightarrow\left(2x+1\right)^2+\left(y-2\right)^2+2\sqrt{\left(4x^2+y^2\right)\left(4x+1\right)}=0\)
\(\Rightarrow\left\{{}\begin{matrix}2x+1=0\\y-2=0\\\left(4x^2+y^2\right)\left(4x+1\right)=0\end{matrix}\right.\)
Hệ đã cho vô nghiệm
Giải hệ phương trình:
1. \(\left\{{}\begin{matrix}x+3=2\sqrt{\left(3y-x\right)\left(y+1\right)}\\\sqrt{3y-2}-\sqrt{\dfrac{x+5}{2}}=xy-2y-2\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}\sqrt{2y^2-7y+10-x\left(y+3\right)}+\sqrt{y+1}=x+1\\\sqrt{y+1}+\dfrac{3}{x+1}=x+2y\end{matrix}\right.\)
3. \(\left\{{}\begin{matrix}\sqrt{4x-y}-\sqrt{3y-4x}=1\\2\sqrt{3y-4x}+y\left(5x-y\right)=x\left(4x+y\right)-1\end{matrix}\right.\)
4. \(\left\{{}\begin{matrix}9\sqrt{\dfrac{41}{2}\left(x^2+\dfrac{1}{2x+y}\right)}=3+40x\\x^2+5xy+6y=4y^2+9x+9\end{matrix}\right.\)
5. \(\left\{{}\begin{matrix}\sqrt{xy+\left(x-y\right)\left(\sqrt{xy}-2\right)}+\sqrt{x}=y+\sqrt{y}\\\left(x+1\right)\left[y+\sqrt{xy}+x\left(1-x\right)\right]=4\end{matrix}\right.\)
6. \(\left\{{}\begin{matrix}x^4-x^3+3x^2-4y-1=0\\\sqrt{\dfrac{x^2+4y^2}{2}}+\sqrt{\dfrac{x^2+2xy+4y^2}{3}}=x+2y\end{matrix}\right.\)
7. \(\left\{{}\begin{matrix}x^3-12z^2+48z-64=0\\y^3-12x^2+48x-64=0\\z^3-12y^2+48y-64=0\end{matrix}\right.\)
Giải hệ phương trình: \(\left\{{}\begin{matrix}x^2-5y^2-8y=3\\\left(2x+4y-1\right)\sqrt{2x-y-1}=\left(4x-2y-3\right)\sqrt{x+2y}\end{matrix}\right.\)
Giải hệ phương trình: \(\left\{{}\begin{matrix}x^3+y^3-4x^2+3y^2+8x+4y-16=0\\\sqrt{x-1}-\sqrt{y+3}=-1\end{matrix}\right.\)
Giải hệ phương trình
\(\left\{{}\begin{matrix}x^3-3x^2y-4x^2+4y^3+16xy=16y^2\\\sqrt{x-2y}+\sqrt{x+y}=2\sqrt{3}\end{matrix}\right.\)
Giải hệ phương trình: \(\left\{{}\begin{matrix}x+\frac{3xy}{\sqrt[3]{x^2-4x+31}}=x^2+y\\y+\frac{3xy}{\sqrt[3]{y^2-4y+31}}=y^2+x\end{matrix}\right.\)
giải hệ phương trình:
1, \(\left\{{}\begin{matrix}2+6y=\frac{x}{y}-\sqrt{x-2y}\\\sqrt{x+\sqrt{x-2y}}=x+3y-2\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^2+y^2+xy+1=4y\\y\left(x+y\right)^2=2x^2-7y+2\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}x^2\left(y+1\right)=6y-2\\x^4y^2+2x^2y^2+y\left(x^2+1\right)=12y^2-1\end{matrix}\right.\)
\(\left\{{}\begin{matrix}y+2\sqrt{x^2+5}=4x+3\\\left(x-3\right)\sqrt{y+4}+\left(y-4\right)\sqrt{x-1}+2\end{matrix}\right.\)
Giải hệ phương trình
giải hệ phương trình
\(\left\{{}\begin{matrix}\sqrt{x-2}+\sqrt{y-3}=3\\2\sqrt{x-2}-3\sqrt{y-3}=-4\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{3x}{x+1}+\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5}{y+4}=4\end{matrix}\right.\)
Giải PT : \(x^2+4x+5=2\sqrt{2x+3}\) Giải hệ PT : \(\left\{{}\begin{matrix}x\left(x+3y\right)=4\\4y^2=5-xy\end{matrix}\right.\)
