# Thread: find the sum of all real roots

1. ## find the sum of all real roots

find the sum of all real roots of this equation
$x + \frac{x}{\sqrt{x^2 - 1}} = 2010$

i think no real roots exist and may be the answer is 0

i got options even
(A)2010
(B)4040
(C)1005
(D)0

2. Originally Posted by grgrsanjay
find the sum of all real roots of this equation
$x + \frac{x}{\sqrt{x^2 - 1}} = 2010$

i think no real roots exist and may be the answer is 0
No, I think it is likely that there are two real roots.
For consider: for x large you have that the second term on the left side is about 1, so you would expect one real solution to be close to 2009.
Also, for x tending to 1 from the right you have that the value of the left side goes to +oo. Hence you can expect another real root to be found close to 1 (but greater than 1).

i got options even
(A)2010
(B)4040
(C)1005
(D)0
Based on my above guesswork I would say that option (A) is right.