Question

Find all solution of the equation.
y=-x
y=xlnx

Answer 1

$\left\{\begin{array}{ccc}y=-x\\y=xlnx\end{array}\right;\ \ \ D:x\in\mathbb{R^+}\\\\xlnx=-x\\\\xlnx+x=0\\\\x(lnx+1)=0\iff x=0\notin D\ or\ lnx+1=0\\\\lnx=-1\iff x=e^{-1}\to x=\frac{1}{e}\in D\\\\Answer:x=\frac{1}{e}\ and\ y=-\frac{1}{e}$