perplexus.info :: Just Math : 2007 And A Real Problem

2007 And A Real Problem (Posted on 2007-09-19)

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.

Submitted by K Sengupta

Rating: 3.2500 (4 votes)

Solution: (Hide)

Substituting x =|u - 2^2007|, the given equation reduces to :
x^2 + x - 2= 0, so that:
x= -2, 1.
Now, |u - 2^2007| = -2 is a contradiction, and so:
u = 2^2007 +/- 1, giving :
The requred sum of the real roots
= (2^2007 +1) + (2^2007 -1)
= 2^2008

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
A little diferent solution	Chesca Ciprian	2007-09-21 16:19:00
Solution	Praneeth	2007-09-20 00:51:11

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