Let y = x/e x.
y'=( 1-x)e^(-x)
X∈(-∞, 1), y'>0, on which the function simply increases, and the range (-∞, 1/e).
X∈( 1, +∞), y'<0, where the function is a simple subtraction with the range of (0, 1/e).
X= 1, y'=0, and the maximum value of the function at x= 1/e.
When x=0, y=0.
(you can make a general picture of y = x/e x from the above)
The previously known equation is: y+ 1/(y- 1)+m=0, that is, y? +(m- 1)y-(m- 1)=0
It is known that the equation must have two real roots y 1, y2 and y 1
Root x 1 (x 1
Roots x2, x3 (0
de(x 1/e x 1)- 1 = y 1- 1,(x2/e x2)- 1 =(x3/e x3)- 1。
Let u=y- 1, then y=u+ 1.
Equation y? +(m- 1)y-(m- 1)=0%: u? +(m+ 1)u+ 1=0
U 1 = Y 1- 1 and U2 = Y2- 1 are its two roots.
u 1 u2= 1
Evaluation formula =(y 1- 1)? (y2- 1)?
=(u 1 u2)? = 1
So choose B.