Problem: The sum of the real values of x satisfying the equality β£x+2β£=2β£xβ2β£ is:
Answer Choices:
A. 31β
B. 32β
C. 6
D. 631β
E. 632β
Solution:
Since 2+2ξ =2(2β2),xξ =2 and since β2+2ξ =β2(β2β2),xξ =β2.
For x>2,x+2=2(xβ2),x=6
For β2<x<2,x+2=β2(xβ2),x=2/3
For x<β2,β(x+2)=β2(xβ2),x=6, a contradiction since 6ξ <β2.
β΄ the sum is 6+2/3=632β