Question

Giải HPT \(\left\{{}\begin{matrix}x+y=70\\xy=1125\end{matrix}\right.\)

Answer 1

Ta có HPT \(\left\{{}\begin{matrix}x+y=70\left(1\right)\\xy=1125\left(2\right)\end{matrix}\right.\)

\(\left(1\right)\Rightarrow x=70-y\) Thay vào hệ \(\left(2\right)\) được :

\(y.\left(70-y\right)=1125\)

\(\Leftrightarrow\left(y-45\right).\left(y-25\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}y=25\\y=45\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=45\\x=25\end{matrix}\right.\)

Vậy pt có nghiệm \(\left(x,y\right)\in\left\{\left(25,45\right);\left(45,25\right)\right\}\)