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\\otin D\ or\ lnx+1=0\\\\lnx=-1\iff x=e^(-1)\to x=(1)/(e)\in D\\\\Answer:x=(1)/(e)\ and\ y=-(1)/(e)`