1,\(\hept{\begin{cases}x^2-2y^2-xy=0\\\sqrt{2x}+\sqrt{y+1}=2\end{cases}}\)
2,\(\hept{\begin{cases}\left(x-y\right)\left(x+y+y^2\right)=x\left(y+1\right)\\\sqrt{x}+\sqrt{y+1}=2\end{cases}}\)
3,\(\hept{\begin{cases}2y^3-\left(x+4\right)y^2+8y+x^2-4x=0\\\sqrt{\frac{1-x}{2}}+\sqrt{x+2y+3}=\sqrt{5}\end{cases}}\)
\(\hept{\begin{cases}\left(x-y\right)^2+4x=4\sqrt{\left(x+1\right)y}-3\\\left(xy-y\right)^2=4\left(y-1\right)\sqrt{2x^2-4}-7\end{cases}}\)
\(\hept{\begin{cases}\left(x-y\right)^2+4x=4\sqrt{\left(x+1\right)y}-3\\\left(xy-y\right)^2=4\left(y-1\right)\sqrt{2x^2-4}-7\end{cases}}\)
\(\hept{\begin{cases}\left(3-x\right)\sqrt{2-x}=2y\sqrt{2y-1}\\\sqrt{x+2}+2\sqrt{y+2}=5\end{cases}}\)
giải hệ
1, \(\hept{\begin{cases}y^6+y^3+2x^2=\sqrt{xy-x^2y^2}\\8xy^3+2y^3+1\ge4x^2+2\sqrt{1+\left(2x-y\right)^2}\end{cases}}\)
2, \(\hept{\begin{cases}x+\frac{y}{\sqrt{1+x^2}+x}+y^2=0\\\frac{x^2}{y^2}+2\sqrt{x^2+1}+y^2=3\end{cases}}\)
\(\hept{\begin{cases}2\left(x+y\right)+\sqrt{x+1}=4\\x+y-3\sqrt{x+y}=-5\end{cases}}\)
Giúp em giải các hệ phương trình này với
a)\(\begin{cases}x^4+2y^3-x=-\dfrac{1}{4}+3\sqrt{3}\\ y^4+2x^3-y=-\dfrac{1}{4}-3\sqrt{3}\end{cases}\)
b) \(\begin{cases} x+\dfrac{78y}{x^2+y^2}=20\\ y+\dfrac{78x}{x^2+y^2}=15\end{cases}\)
c) \(\begin{cases}\left(1-\dfrac{12}{y+3x}\right)\cdot \sqrt{x}=2\\ \left(1+\dfrac{12}{y+3x}\right)\cdot\sqrt{y}=6 \end{cases}\)
d) \(\begin{cases} \sqrt{x+1}+\sqrt[4]{x-1}-\sqrt{y^4+2}=y\\ x^2+2x(y-1)+y^2-6y+1=0\end{cases}\)
e) \(\begin{cases} \sqrt{4x^2+(4x-9)(x-y)}+\sqrt{xy}=3y\\ 4\sqrt{(x+2)(y+2x)}=3(x+3)\end{cases}\)
\(\hept{\begin{cases}x\sqrt{4x^2+y^2}+\sqrt{4-y^2}=x^2+1\\\left(5x^2+y^2\right)^2=25+2\sqrt{xy}\left(5-5x^2-y^2\right)\end{cases}}\)
\(\hept{\begin{cases}\sqrt{x}+\sqrt{y}+\sqrt{\left(x-1\right)\left(y+1\right)}+y=7\\\left(x-y\right)\sqrt{y}+y\sqrt{x-y}+1=x+\sqrt{xy-y^2}\end{cases}}\)