\(\left\{{}\begin{matrix}x^2+y^2-xy=2\left(1\right)\\x+y=x^3\left(2\right)\end{matrix}\right.\)
Nhân theo vế của (1) vs 2():
\(\left(x+y\right)\left(x^2-xy+y^2\right)=2x^3\)
\(\Leftrightarrow x^3+y^3=2x^3\Leftrightarrow x^3=y^3\Leftrightarrow x=y\)
Thay vào pt ta tìm đc x y
Giải HPT: \(\left\{{}\begin{matrix}x^2+2y^2=3\\x+y^2+xy=1\end{matrix}\right.\)
giải hpt :\(\left\{{}\begin{matrix}xy=6\\x^2+x+y+y^2=18\end{matrix}\right.\)
Giải hệ phương trình
\(\left\{{}\begin{matrix}x^2+y^2+xy=13\\x^4+y^4+x^2y^2=91\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+y\right)^2-xy=13\\\left(x^2+y^2\right)^2-\left(xy\right)^2=91\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+y\right)^2=13+xy\\\left[\left(x+y\right)^2-2xy\right]^2-\left(xy\right)^2=91\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+y\right)^2-xy=13\\\left(13-xy\right)^2-\left(xy\right)^2=91\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}xy=3\\\left(x+y\right)^2=16\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y=4\\xy=3\end{matrix}\right.\) hoặc x+y = -4
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+y=4\\xy=3\end{matrix}\right.\\\left\{{}\begin{matrix}x+y=-4\\xy=3\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\\\left\{{}\begin{matrix}x=-3\\y=-1\end{matrix}\right.\end{matrix}\right.\)hoặc \(\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)hoặc \(\left\{{}\begin{matrix}x=-1\\y=-3\end{matrix}\right.\)
Mọi người có thể giải thích từ dấu tương đương thứ 3 xuống 4. tại sao lại như vậy k?
giải hpt \(\left\{{}\begin{matrix}\dfrac{1-xy}{x\left(1+y^2\right)}=\dfrac{2}{5}\\\dfrac{1-xy}{y\left(1+x^2\right)}=\dfrac{1}{2}\end{matrix}\right.\)
Giải hpt.
\(\left\{{}\begin{matrix}x^2+y^2+xy=1\\x^3+y^3=x+7y\end{matrix}\right.\)
Giải hpt \(\left\{{}\begin{matrix}x^2+x^3y-xy^2+xy-y=1\\x^4+y^2-xy\left(2x-1\right)=1\end{matrix}\right.\)
giải hpt
\(\left\{{}\begin{matrix}x^2+\left(y+1\right)^2=xy+x+1\\2x^3=x+y+1\end{matrix}\right.\)
Giải hpt : \(\left\{{}\begin{matrix}x^2+y^2-2y-6+2\sqrt{2y+3}=0\\\left(x-y\right)\left(x^2+xy+y^2+3\right)=3\left(x^2+y^2\right)+2\end{matrix}\right.\)
giải hpt: \(\left\{{}\begin{matrix}\sqrt{xy+\left(x-y\right)\left(\sqrt{xy}-2\right)}+\sqrt{x}=y+\sqrt{y}\\\left(x+1\right)\left(y+\sqrt{xy}+x-x^2\right)=4\end{matrix}\right.\)
