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.

The equation can be write like this :

u^2-2^2007.u-2^2007.u + |u-2^2007|+2^4014-2=0 or

u(u-2^2007)-2^2007(u-2^2007)+|u-2^2007| - 2 =0 or

(u-2^2007)^2+|u-2^2007|-2=0

with the notation t=|u-2^2007| and t>0 we have

t^2+t-2=0 with t=1 and so we have

u(1)=2^2007+1 and u(2)=2^2007-1

and the answer is 2x2^2007 = 2^2008

Posted by Chesca Ciprian on 2007-09-21 16:19:00