Question

Giải hpt:    

\(\hept{\begin{cases}X^2-xy+y^2=7\\x^4+x^2y^2+y^4=21\end{cases}}\)

 

Answer 1

\(\Leftrightarrow\hept{\begin{cases}\left(x^2+y^2\right)-xy=7\\\left(x^2+y^2\right)^2-x^2y^2=21\end{cases}}\)

Đặt \(\hept{\begin{cases}a=x^2+y^2\\b=xy\end{cases}}\)

Hệ trở thành \(\hept{\begin{cases}a-b=7\\a^2-b^2=21\end{cases}\Leftrightarrow}\hept{\begin{cases}a-b=7\\\left(a+b\right)\left(a-b\right)=21\end{cases}\Leftrightarrow}\hept{\begin{cases}a-b=7\\a+b=3\end{cases}}\Leftrightarrow\hept{\begin{cases}a=5\\b=-2\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x^2+y^2=5\\xy=-2\end{cases}}\)