Determine the sum of the real roots of this equation:

u² – 2²⁰⁰⁸.u + | u – 2²⁰⁰⁷| + 2(2⁴⁰¹³ - 1) = 0

Note:|x| denotes the absolute value of x.

Case(i): If u ≥ 2^2007,|u-2007|=u-2007. 
The equation becomes

u²-2^2008.u+u-2^2007+2(2^4013-1)=0
u²-(2^2008-1) u+2^4014-2^2007-2=0
The roots to equation will be
(-b+/- √b²-4ac)/2 = 2^2007+1 and 2^2007-1
As 2^2007-1 < 2^2007, it wont solution for this case.
u=2^2007+1
Case(ii): Similarly, the solution for the other case will be 2^2007-1
Sum of real roots=2^2007+1+2^2007-1=2^2008

Posted by Praneeth on 2007-09-20 00:51:11