\(x^2+2xy+y^2+2x+2y=8\)
\(\Leftrightarrow\left(x+y\right)^2+2\left(x+y\right)-8=0\)
\(\Leftrightarrow\left(x+y-2\right)\left(x+y+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+y=2\\x+y=-4\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}y=2-x\\y=-4-x\end{matrix}\right.\) thay vào pt ban đầu:
\(\left[{}\begin{matrix}x+3\left(2-x\right)=2018\\x+3\left(-4-x\right)=2018\end{matrix}\right.\)
Giải các hệ phương trình sau:
a) \(\left\{{}\begin{matrix}4x^2-4xy-14x-3y^2+y+10=0\\5\sqrt{xy}+2x+2y=6\sqrt{y}-8\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}2x^4+3x^2y+4x^2-2y^2+3y+2=0\\\sqrt{x\left(y-1\right)}+2y+2\sqrt{y-1}=3x+2\sqrt{x}+2\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}x^6+3x^2-y^3-6y^2-15y-14=0\\\sqrt{xy+2x-y-2}+6x-2y=10\end{matrix}\right.\)
d) \(\left\{{}\begin{matrix}xy+x+y=x^2-2y^2\\x\sqrt{2y}-y\sqrt{x-1}=2x-2y\end{matrix}\right.\)
mọi người giải gúp mình với. Cần cực gấp \(a,\left\{{}\begin{matrix}3x+2y=-2\\-x+4y=3\end{matrix}\right.b,\left\{{}\begin{matrix}x+2y=11\\5x-3y=3\end{matrix}\right.c,\left\{{}\begin{matrix}10x-9y=1\\15x+21y=36\end{matrix}\right.d,\left\{{}\begin{matrix}2x+y=3\\x+y=2\end{matrix}\right.e,\left\{{}\begin{matrix}x+y=2\\2x-3y=9\end{matrix}\right.f,\left\{{}\begin{matrix}x-2y=11\\5x+3y=3\end{matrix}\right.g,\left\{{}\begin{matrix}3x-y=5\\2x+3y=18\end{matrix}\right.h,\left\{{}\begin{matrix}5x+3y=-7\\3x-y=-8\end{matrix}\right.\)
giải hệ:
a) \(\left\{{}\begin{matrix}\sqrt{x+3y}+\sqrt{x+y}=2\\\sqrt{x+y}+y-x=1\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x+y+\frac{1}{x}+\frac{1}{y}=4\\x^2+y^2+\frac{1}{x^2}+\frac{1}{y^2}=4\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}\left(x-\frac{1}{y}\right)\left(y+\frac{1}{x}\right)=2\\2x^2y+xy^2-4xy=2x-y\end{matrix}\right.\)
d) \(\left\{{}\begin{matrix}2x^2+xy=y^2-3y+2\\x^2-y^2=3\end{matrix}\right.\)
e) \(\left\{{}\begin{matrix}x^2+y^2+z^2+2xy-xz-zy=3\\x^2+y^2-2xy-xz+zy=-1\end{matrix}\right.\)
f) \(\left\{{}\begin{matrix}x^2-y^2+5x-y+6=0\\x^2+\left(x-y\right)^2=2+\sqrt{6x+7}+2\sqrt{x+y+1}\end{matrix}\right.\)
Giải hệ phương trình :
a) \(\left\{{}\begin{matrix}x^2+y^2=1\\x^2+y^2=1\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{y}+\sqrt{z}=2014\\\dfrac{1}{3x+2y}+\dfrac{1}{3y+2z}+\dfrac{1}{3z+2x}=\dfrac{1}{x+2y+3z}+\dfrac{1}{y+2x+3x}+\dfrac{1}{z+2x+3y}\end{matrix}\right.\)
giải hệ
a,\(\left\{{}\begin{matrix}\left(x+y\right)\left(x^2+y^2\right)=15\\\left(x-y\right)\left(x^2-y^2\right)=3\end{matrix}\right.\)
b,\(\left\{{}\begin{matrix}x^3-y^3=9\\x^2+2y^2=x-4y\end{matrix}\right.\)
c,\(\left\{{}\begin{matrix}\left(x-y\right)\left(2x+3y\right)=12\\6\left(x-y\right)+xy\left(x-y\right)=12\end{matrix}\right.\)
d,\(\left\{{}\begin{matrix}x^2+y^2+1=2\left(x+y\right)\\y\left(2x-y\right)=\left(2y+1\right)\end{matrix}\right.\)
Giải hệ phương trình
\(\left\{{}\begin{matrix}x-y=2\\3x+2y=11\end{matrix}\right.\)
giải hệ pt sau
\(\left\{{}\begin{matrix}x^2+2xy+2y^2=9\\2y^2+2xy+y^2=2\end{matrix}\right.\)
Giải hệ phương trình \(\left\{{}\begin{matrix}\left(x-1\right)^2=2y\\\left(y-1\right)^2=2z\\\left(z-1\right)^2=2x\end{matrix}\right.\)
1. \(\left\{{}\begin{matrix}x+xy+y=11\\x^2+y^2-xy-2\left(x+y\right)=-31\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}xy-x+y=-3\\x^2+y^2-x+y+xy=6\end{matrix}\right.\)
3. \(\left\{{}\begin{matrix}x^2+4y^2=8\\x+2y=4\end{matrix}\right.\)
4. \(\left\{{}\begin{matrix}2+6y=\frac{x}{y}-\sqrt{x-2y}\\\sqrt{x+\sqrt{x-2y}}=x+3y-2\end{matrix}\right.\)
