• # question_answer If x, $y\in R$ and $x-y=2$ then minimum value of  $x+y+xy$ is A) 2 B) $-\,2$ C) 0 D) 1

 $x-y=2$ $x+y+xy$ is to be minimized. Putting  $y=x-2.$ we get, $f\,(x)=2x-2+x\,(x-2)$
 $f'\,(x)=2+2x-2=0$       at $x=0.$ $f''\,(x)=2$$\Rightarrow$$x=0$ is a point of minima Thus minimum value is at $x=0$ & $y=-\,2.$ Hence [B] is correct.