ta có  \(7x^2-13xy-2y^2=0\)

  \(7x^2-14xy+xy-2y^2=0\)

7x(x-2y)+y(x-2y)=0

(7x+y)(x-2y)=0

=>. 7x+y=0   hoặc   x-2y=0

=>   y=-7x     hoặc x=2y

Thay lần lượt vào A là OK nha bn !

\(\hept{\begin{cases}xy^2-3xy+3x-2y+2=0\\x^2+y^2+xy-7x-6y+14=0\end{cases}}\)

HPT \(\Leftrightarrow\hept{\begin{cases}x\left(y^2-4y+4\right)+xy-x-2y+2=0\\\left(x^2-4x+4\right)+\left(y^2-4y+4\right)+xy-2x-2y+4-x+2=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x\left(y-2\right)^2+\left(x-2\right)\left(y-2\right)+\left(x-2\right)=0\\\left(x-2\right)^2+\left(y-2\right)^2+\left(x-2\right)\left(y-2\right)-\left(x-2\right)=0\end{cases}}\)

Đặt a = x - 2 ; b = y - 2 ta có :

\(\hept{\begin{cases}\left(a+2\right)b^2+ab+a=0\\a^2+b^2+ab-a=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}a\left(b^2+b+1\right)=-2b^2\\a=a^2+b^2+ab\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}a=\frac{-2b^2}{b^2+b+1}\le0\forall b\\a=a^2+b^2+ab\ge0\forall ab\end{cases}}\)

\(\Rightarrow a=0\Rightarrow b=0\Rightarrow x=y=2\left(TM\right)\)

hướng dẫn thôi tự trình bày lại nhé

pt đầu bài \(\Leftrightarrow\)\(4x^2+9y^2+25+12xy+20x+30y=-3x^2+24x+36y+40\)

\(\Leftrightarrow\)\(\left(2x+3y+5\right)^2-12\left(2x+3y+5\right)+36=-3x^2+16\)

\(\Leftrightarrow\)\(\left(2x+3y-1\right)^2=-3x^2+16\le16\)

\(\Leftrightarrow\)\(-4\le2x+3y-1\le4\)\(\Leftrightarrow\)\(2\le2x+3y+5\le10\)

\(\Rightarrow\)\(\hept{\begin{cases}S_{min}=2\left(x=0;y=-1\right)\\S_{max}=10\left(x=0;y=\frac{5}{3}\right)\end{cases}}\)

\(\left\{{}\begin{matrix}6x^2-y^2+xy-6y-12x=0\left(1\right)\\4x^2-xy+9=0\left(2\right)\end{matrix}\right.\)

Ta có:

\(\left(1\right)\Leftrightarrow\left(2x+y\right)\left(3x-y-6\right)=0\)

\(\left[{}\begin{matrix}y=-2x\\y=6-3x\end{matrix}\right.\)

Thế lại vô (2) rồi làm tiếp sẽ ra.