Question

x(x+y)=2

Answer 1

x(x+y)=2

=>\(\left(x;x+y\right)\in\left\{\left(1;2\right);\left(2;1\right);\left(-1;-2\right);\left(-2;-1\right)\right\}\)

TH1: \(\left\{{}\begin{matrix}x=1\\x+y=2\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=1\\y=2-x=2-1=1\end{matrix}\right.\)

TH2: \(\left\{{}\begin{matrix}x=2\\x+y=1\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=2\\y=1-x=1-2=-1\end{matrix}\right.\)

TH3: \(\left\{{}\begin{matrix}x=-1\\x+y=-2\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=-1\\y=-2-x=-2-\left(-1\right)=-1\end{matrix}\right.\)

TH4: \(\left\{{}\begin{matrix}x=-2\\x+y=-1\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=-2\\y=-1-x=-1-\left(-2\right)=-1+2=1\end{matrix}\right.\)