b) \(\left\{{}\begin{matrix}\left(x-1\right)^2-2y=2\\\left(x+1\right)^2+3y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3\left(x+1\right)^2-6y=6\left(1\right)\\2\left(x-1\right)^2+6y=2\left(2\right)\end{matrix}\right.\)
Cộng theo vế 2 pt trên, ta có
\(3\left(x+1\right)^2+2\left(x-1\right)^2=8\)
\(\Leftrightarrow5x^2+2x-3=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{5}\\x=-1\end{matrix}\right.\)
Từ đó dễ dàng tìm được y.
a) \(\left\{{}\begin{matrix}\left(x+y\right)^2=50\left(1\right)\\x+5\left(y-1\right)=xy\left(2\right)\end{matrix}\right.\)
Ta viết lại pt (2)
\(x+5\left(y-1\right)=xy\)
\(\Leftrightarrow\left(x-xy\right)+5\left(y-1\right)=0\)
\(\Leftrightarrow x\left(1-y\right)-5\left(1-y\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(1-y\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\y=1\end{matrix}\right.\)
- TH1: Thay x = 5 vào pt (1) tìm được \(\left[{}\begin{matrix}y=-5+5\sqrt{2}\\y=-5-5\sqrt{2}\end{matrix}\right.\)
- TH2: Thay y = 1 vào pt (1) tìm được \(\left[{}\begin{matrix}x=-1+5\sqrt{2}\\x=-1-5\sqrt{2}\end{matrix}\right.\)