\(\Leftrightarrow\left\{{}\begin{matrix}x^2+z^2=\frac{17}{4}\\2xy+4y=\frac{5}{2}\\5y^2+4z=-\frac{27}{4}\end{matrix}\right.\)
\(\Rightarrow x^2+z^2-2xy-4y+5y^2+4z=-5\)
\(\Leftrightarrow\left(x-y\right)^2+\left(z+2\right)^2+\left(2y-1\right)^2=0\)
\(\Rightarrow\left\{{}\begin{matrix}x=\frac{1}{2}\\z=-2\\y=\frac{1}{2}\end{matrix}\right.\) \(\Rightarrow M=...\)
\(\left\{{}\begin{matrix}x=4y^2\left(1-x\right)\\y=4z^2\left(1-y\right)\\z=4x^2\left(1-z\right)\end{matrix}\right.\)
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. \(\left\{{}\begin{matrix}x^3-12z^2+48z-64=0\\y^3-12x^2+48x-64=0\\z^3-12y^2+48y-64=0\end{matrix}\right.\)
Tìm x,y,z thỏa mãn điều kiện: \(\left\{{}\begin{matrix}x+y=\sqrt{4z-1}\\y+z=\sqrt{4x-1}\\z+x=\sqrt{4y-1}\end{matrix}\right.\)
Hai số thực x,y thỏa mãn hệ điều kiện \(\left\{{}\begin{matrix}x^3+2y^2-4y+3=0\\x^2+x^2y^2-2y=0\end{matrix}\right.\)
Tính giá trị biểu thức \(P=x^2+y^2\)
Giaỉ hệ phương trình
1) \(\left\{{}\begin{matrix}x^2-2xy+x+y=0\\x^4-x^2\left(4y-3\right)+y^2=0\end{matrix}\right.\)
2)\(\left\{{}\begin{matrix}3x^2+2xy+y^2=11\\x^2+2xy+3y^2=17\end{matrix}\right.\)
3)\(\left\{{}\begin{matrix}x^3-2y^3-x-4y=0\\13x^2-41xy+21y^2+9=0\end{matrix}\right.\)
giải hệ phương trình
a) \(\left\{{}\begin{matrix}3x-2y+z=14\\2x+y-z=3\\z-2x=-5\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x^2-y^2=4y+2x+3\\x^2+2x+y=0\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}\left|xy-4\right|=8-y^2\\xy=2+x^2\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{4x}{1+4x}=\sqrt{y}\\\dfrac{4y}{1+4y}=\sqrt{z}\\\dfrac{4z}{1+4z}=\sqrt{x}\end{matrix}\right.\)
Giải phương trình bằng phương pháp thế :
1) \(\left\{{}\begin{matrix}4x+y=2\\8x+3y=5\end{matrix}\right.\)
2) \(\left\{{}\begin{matrix}x-y=m\\2x+y=4\end{matrix}\right.\)
3)\(\left\{{}\begin{matrix}3x+2y=6\\x-y=2\end{matrix}\right.\)
4) \(\left\{{}\begin{matrix}2x-3y=1\\-4x+6y=2\end{matrix}\right.\)
5)\(\left\{{}\begin{matrix}2x+3y=5\\5x-4y=1\end{matrix}\right.\)
6)\(\left\{{}\begin{matrix}3x-y=7\\x+2y=0\end{matrix}\right.\)
7)\(\left\{{}\begin{matrix}x+4y=2\\3x+2y=4\end{matrix}\right.\)
8)\(\left\{{}\begin{matrix}-x-y=2\\-2x-3y=9\end{matrix}\right.\)
9)\(\left\{{}\begin{matrix}2x-3y=2\\-4x+6y=2\end{matrix}\right.\)
giúp mình với :((
Giải các hệ phương trình sau bằng phương pháp thế:
a) \(\left\{{}\begin{matrix}x-y=3\\3x-4y=2\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}7x-3y=5\\4x+y=2\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}x+3y=-2\\5x-4y=11\end{matrix}\right.\)
