Question

cho biết x^2-y^2=16 và x-y=2. tìm x và y

Answer 1

\(x^2-y^2=16\\ \Leftrightarrow\left(x-y\right)\left(x+y\right)=16\\ \Leftrightarrow2\left(x+y\right)=16\\ \Leftrightarrow x+y=8\)

Mà \(x-y=2\Leftrightarrow\left\{{}\begin{matrix}x=\left(8+2\right):2=5\\y=8-5=3\end{matrix}\right.\)

Answer 2

\(x^2-y^2=16\)

\(\left(x+y\right)\left(x-y\right)=16\)

\(2\left(x+y\right)=16\) ( Vì \(x-y=2\) )

\(x+y=8\)

⇒\(\left\{{}\begin{matrix}x-y=2\\x+y=8\end{matrix}\right.\)

⇒\(\left\{{}\begin{matrix}x=5\\y=3\end{matrix}\right.\)