\(\Leftrightarrow\left\{{}\begin{matrix}x^3-y^3=35\\6x^2+9y^2=12x-27y\end{matrix}\right.\)
\(\Rightarrow x^3-y^3-6x^2-9y^2=35-12x+27y\)
\(\Leftrightarrow x^3-6x^2+12x-8=y^3+9y^2+27y+27\)
\(\Leftrightarrow\left(x-2\right)^3=\left(y+3\right)^3\)
\(\Leftrightarrow x-2=y+3\)
\(\Leftrightarrow y=x-5\)
Thay vào pt dưới: \(2x^2+3\left(x-5\right)^2=4x-9\left(x-5\right)\)
\(\Leftrightarrow...\)
giải hpt:
a) \(\left\{{}\begin{matrix}4x+9y=6\\3x^2+6xy-x+3y=0\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}\left(x+y+2\right)\left(2x+2y-1\right)=0\\3x^2-32y^2+5=0\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}2x^2-xy+3y^2=7x+12y-1\\x-y+1=0\end{matrix}\right.\)
Bài 4 Đoán nghiệm của các hệ phương trình sau :
a)\(\left\{{}\begin{matrix}y=3-4x\\\\y=3x-1\end{matrix}\right.\) b)\(\left\{{}\begin{matrix}3y=2x\\\\2y=-3x\end{matrix}\right.\) c)\(\left\{{}\begin{matrix}2x-y=1\\\\x-2y=-1\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}\frac{1}{3}x-y=\frac{2}{3}\\\\x-3y=2\end{matrix}\right.\) e)\(\left\{{}\begin{matrix}4x-4y=2\\\\-2x+2y=-1\end{matrix}\right.\)
giúp mik giải bài hệ pt vs ạ!
1,\(\left\{{}\begin{matrix}x^2+y^2+\dfrac{2xy}{x+y}=1\\\sqrt{x+y}=x^2-y\end{matrix}\right.\)
2,\(\left\{{}\begin{matrix}2x^3+xy^2+x=y^3+4x^2y+2y\\\sqrt{4x^2+x+6}-5\sqrt{1+2y}=1-4y\end{matrix}\right.\)
3,\(\left\{{}\begin{matrix}2x^2+\sqrt{2}x=\left(x+y\right)y+\sqrt{x+y}\\\sqrt{x-1}+xy=\sqrt{y^2+21}\end{matrix}\right.\)
4,\(\left\{{}\begin{matrix}\sqrt{9y^2+\left(2y+3\right)\left(y-x\right)}+4\sqrt{xy}=7x\\\left(2y-1\right)\sqrt{1+x}+\left(2y+1\right)\sqrt{1-x}=2y\end{matrix}\right.\)
giải hệ phương trình
1, \(\left\{{}\begin{matrix}2x^2+3y=17\\3x^2-2y=6\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}\left|x-1\right|+\left|y-1\right|=2\\4\left|x-1\right|+3\left|y-1\right|=7\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}3\sqrt{x-1}+2\sqrt{y}=2\\2\sqrt{x-1}-\sqrt{y}=4\end{matrix}\right.\)
4 , \(\left\{{}\begin{matrix}x+y=2\\\left|2x-3y\right|=1\end{matrix}\right.\)
5 , \(\left\{{}\begin{matrix}2x-y=1\\\left|x-y\right|=\left|2y-1\right|\end{matrix}\right.\)
6,\(\left\{{}\begin{matrix}\left(x-3\right)\left(y+6\right)=xy\\\left(x+2\right)\left(y-2\right)=xy\end{matrix}\right.\)
7 , \(\left\{{}\begin{matrix}\left(x-3\right)\left(2y+5\right)=\left(2x+7\right)\left(y-1\right)\\\left(4x+1\right)\left(3y-6\right)=\left(6x-1\right)\left(2y+3\right)\end{matrix}\right.\)
8 , \(\left\{{}\begin{matrix}4x^2-5\left(y+1\right)=\left(2x-3\right)^2\\3\left(7x+2\right)=5\left(2y-1\right)-3x\end{matrix}\right.\)
Giải hệ
a) \(\left\{{}\begin{matrix}x^2\left(y^2+1\right)+2y\left(x^2+x+1\right)=3\\\left(x^2+x\right)\left(y^2+y\right)=1\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}\left(6x+5\right)\sqrt{2x+1}-2y-3y^3=0\\y+\sqrt{x}=\sqrt{2x^2+4x-23}\end{matrix}\right.\)
Giải bất pt
\(\dfrac{9}{\left|x-5\right|-3}\ge\left|x-2\right|\)
Giải hệ pt
a) \(\left\{{}\begin{matrix}x^2+2xy^2=3\\y^3+y+x\left(2xy-1\right)=3\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x^2+x^3y-xy^2+xy-y=1\\x^4+y^2-xy\left(2x-1\right)=1\end{matrix}\right.\)
Giải hệ phương trình \(\left\{{}\begin{matrix}2x^3+9x^2+12x=y^3+3y^2+4y+15\\2y^3+9y^2+12y=z^3+3z^2+4z+15\\2z^{^3}+9z^2+12z=x^3+3x^2+4x+15\end{matrix}\right.\)