Question

[Ăâêưưgcg]

Giải hệ n giúp mk vs

xy+x+y=71

x²y+xy²=880

(đừng giải theo viét mk k hiểu vì mk chưa học, mong mn thông cảm)

Answer 1

[bach nhac lam]

\(\Rightarrow\left\{{}\begin{matrix}x+y=71-xy\\xy\left(x+y\right)=880\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x+y=71-xy\\xy\left(71-xy\right)=880\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x+y=71-xy\\x^2y^2-71xy+880=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x+y=71-xy\\\left(xy-16\right)\left(xy-55\right)=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x+y=71-xy\\\left[{}\begin{matrix}xy=16\\xy=55\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}xy=55\\x+y=16\end{matrix}\right.\\\left\{{}\begin{matrix}xy=16\\x+y=55\end{matrix}\right.\end{matrix}\right.\)

+ TH1: \(\left\{{}\begin{matrix}xy=55\\x+y=16\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=\frac{55}{x}\\x+\frac{55}{x}=16\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=\frac{55}{x}\\x^2-16x+55=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}y=\frac{55}{x}\\\left(x-5\right)\left(x-11\right)=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=5\\y=11\end{matrix}\right.\\\left\{{}\begin{matrix}x=11\\y=5\end{matrix}\right.\end{matrix}\right.\)

TH còn lại lm tương tự

Answer 2

[Ăâêưưgcg]

cảm ơn bn nhìu