[tex]2\sqrt{x^{2} + 4x + 4 } + \sqrt{1005^{2} + 2 * 1005 * 1006 + 1006^{2} } = \sqrt{2013 + 2 + 4 + ... + 4024}\\ <=> 2\sqrt{(x + 2)^{2} } + \sqrt{(1005 + 1006)^{2} } = \sqrt{2013 + 2 (1 + 2 + 3 + ... + 2010 + 2011 + 2012)}\\ <=> 2(x+2) + 1005 + 1006 = \sqrt{2013 + 2(\frac{2012(2012 + 1)}{2} )} \\<=> 2x +4 + 1005 + 1006 = \sqrt{2013 + 2012(2012 + 1)} \\ <=> 2x + 2015 = \sqrt{2013 + 2012* 2013} \\<=> 2x + 2015 = \sqrt{2013(1 + 2012) } \\<=> 2x + 2015 = \sqrt{2013 * 2013}\\ <=> 2x + 2015 = \sqrt{2013^{2} }[/tex]
[tex]<=> 2x + 2015 = 2013\\<=> 2x = 2013 - 2015\\<=> 2x = -2 => x = -1\\S = {-1}[/tex]
