\(x^2+y^2-xy=x+y+2\)
\(\Leftrightarrow2x^2+2y^2-2xy-2x-2y-4=0\)
\(\Leftrightarrow\left(x-y\right)^2+\left(x-1\right)^2+\left(y-1\right)^2=6\)
Vì \(\left(x-y\right)^2+\left(y-1\right)^2\ge0\forall x;y\)
\(\Rightarrow\left(x-1\right)^2\le6\forall x\)
\(\Rightarrow-\sqrt{6}\le x-1\le\sqrt{6}\)
\(\Leftrightarrow x\in\left\{-1;0;1;2;3\right\}\)
Từ đó thay vào tìm các giá trị tương ứng của y.
Cho he phuong trinh: \(\left\{{}\begin{matrix}x-2y=3-m\\2x+y=3.\left(m+2\right)\end{matrix}\right.\)
Goi (x;y) la nghiem cua he phuong trinh. Tim m de \(x^2+y^2\) dat GTNN
tim x y thoa man:2\(\left(x\sqrt{y-4}+y\sqrt{x-4}\right)=xy\\\)
Giải các hệ phương trình
a) \(\left\{{}\begin{matrix}x+y+xy=3\\x^2y+xy^2=2\end{matrix}\right.\) b) \(\left\{{}\begin{matrix}x^2+y^2=2\left(xy+2\right)\\x+y=6\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}x^2-2x=y\\y^2-2y=x\end{matrix}\right.\) d) \(\left\{{}\begin{matrix}2x^2-xy+3y^2=13\\x^2+4xy-2y^2=-6\end{matrix}\right.\)
e) \(\left\{{}\begin{matrix}2x^2-y^2=1\\xy+x^2=2\end{matrix}\right.\) f) \(\left\{{}\begin{matrix}x^2-y^2=1-xy\\x^2+y^2=3xy+11\end{matrix}\right.\)
Cần gấp lắm, ai giúp với
Giải hệ PT:
\(\left\{{}\begin{matrix}x^2-xy+y^2=3\left(x-y\right)\\x^2+xy+y^2=7\left(x-y\right)^3\end{matrix}\right.\)
Giải các phương trình sau:
a.{\(\dfrac{3x+1}{2}-\dfrac{y-2}{3}=4\)
{\(\dfrac{x-2}{3}+\dfrac{y+1}{4}=5\)
b.{(x + 5) (y - 4) = xy
{(x + 5) (y + 12) = xy
cho he phuong trinh \(\left\{{}\begin{matrix}x-y-m+6=0\\\left(m+3\right)x-2y-4m+13=0\end{matrix}\right.\)
Tim m de he phuong trinh co nghiem duy nhat, voi dieu kien do, tim he thuc lien he giua x va y khong phu thuoc vao m
Giải các hệ phương trình
a) \(\left\{{}\begin{matrix}x+y+xy=3\\x^2y+xy^2=2\end{matrix}\right.\) b) \(\left\{{}\begin{matrix}x^2+y^2=2\left(xy+2\right)\\x+y=6\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}x^2-2x=y\\y^2-2y=x\end{matrix}\right.\) d) \(\left\{{}\begin{matrix}2x^2-xy+3y^2=13\\x^2+4xy-2t^2=-6\end{matrix}\right.\)
e) \(\left\{{}\begin{matrix}2x^2-y^2=1\\xy+x^2=2\end{matrix}\right.\)
Giải hệ phương trình
a, \(\left\{{}\begin{matrix}\left(x+1\right)\left(y+1\right)=8\\x\left(x+1\right)+y\left(y+1\right)+xy=17\end{matrix}\right.\)
b, \(\left\{{}\begin{matrix}x+y+xy=3\\x^2+y^2=2\end{matrix}\right.\)
c, \(\left\{{}\begin{matrix}x^2+y^2+xy=4\\x-y-3xy=16\end{matrix}\right.\)
GIÚP MÌNH NHÉ
Giải hệ pt:
a)\(\left\{{}\begin{matrix}x^2+y^2+x+y=18\\x\left(x+1\right).y\left(y+1\right)=72\end{matrix}\right.\) b) \(\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{y+1}=1\\3y-1=xy\end{matrix}\right.\) c)\(\left\{{}\begin{matrix}2x+3y=xy+5\\\frac{1}{x}+\frac{1}{y+1}=1\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}\sqrt{\frac{x}{y}}-3\sqrt{\frac{y}{x}}=2\\x-y+xy=1\end{matrix}\right.\) e)\(\left\{{}\begin{matrix}xy+x+y=x^2-2y^2\\x\sqrt{2y}-y\sqrt{x-1}=2x-2y\end{matrix}\right.\)
HELP ME :((
