giải các HPT sau:
a) \(\left\{{}\begin{matrix}x^2+y^2=8\\x+2y=4\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x^2-xy=24\\2x-3y=1\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}x^2-3xy+y^2+2x+3y-6=0\\2x-y=3\end{matrix}\right.\)
d) \(\left\{{}\begin{matrix}\left(x-y\right)^2=49\\3x+4y=84\end{matrix}\right.\)
d)
\(\left\{{}\begin{matrix}\left(x-y\right)^2=49\\3x+4y=84\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x-y=7\\x-y=-7\end{matrix}\right.\\3x+4y=84\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-y=7\\3x+4y=84\end{matrix}\right.\\\left\{{}\begin{matrix}x-y=-7\\3x+4y=84\end{matrix}\right.\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=16\\y=9\end{matrix}\right.\\\left\{{}\begin{matrix}x=8\\y=15\end{matrix}\right.\end{matrix}\right.\)
=> Hệ phương trình có nghiệm (x;y)= (16;9) hoặc (x;y)=(8;15)
a, \(\left\{{}\begin{matrix}x^2+y^2=8\\x+2y=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(4-2y\right)^2+y^2=8\\x=4-2y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5y^2-16y+8=0\\x=4-2y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}y=\frac{8+2\sqrt{6}}{5}\\y=\frac{8-2\sqrt{6}}{5}\end{matrix}\right.\\x=4-2y\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\frac{4-4\sqrt{6}}{5}\\y=\frac{8+2\sqrt{6}}{5}\end{matrix}\right.\\\left\{{}\begin{matrix}x=\frac{4+4\sqrt{6}}{5}\\y=\frac{8-2\sqrt{6}}{5}\end{matrix}\right.\end{matrix}\right.\)
b, \(\left\{{}\begin{matrix}x^2-xy=24\\2x-3y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x^2-3xy=72\\3y=2x-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x^2-x\left(2x-1\right)=72\\3y=2x-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2+x-72=0\\3y=2x-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-8\right)\left(x+9\right)=0\\3y=2x-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=8\\x=-9\end{matrix}\right.\\3y=2x-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=8\\y=5\end{matrix}\right.\\\left\{{}\begin{matrix}x=-9\\y=-\frac{19}{3}\end{matrix}\right.\end{matrix}\right.\)
c, \(\left\{{}\begin{matrix}x^2-3xy+y^2+2x+3y-6=0\\2x-y=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2-3x\left(2x-3\right)+\left(2x-3\right)^2+2x+3\left(2x-3\right)-6=0\\y=2x-3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2-3x+6=0\\y=2x-3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-\frac{3}{2}\right)^2=-\frac{15}{4}\\y=2x-3\end{matrix}\right.\)
\(\Rightarrow\) Hệ phương trình vô nghiệm
