Question 30455
I get 1 solution 
(B) is the answer
{{{sqrt(x-4) - sqrt(x+8) = 2}}}
{{{sqrt(x - 4) = 2 + sqrt(x + 8)}}}
square both sides
{{{x - 4 = 4 + 4* sqrt(x + 8) + x + 8}}}
cancel x's, combine terms
{{{4*sqrt(x + 8) = -16}}}
{{{sqrt(x + 8) = -4}}}
square both sides
{{{x + 8 = 16}}}
{{{x = 8}}}
check
sqrt(8-4) - sqrt(8+8) = 2
{{{0 +- sqrt(4) - 0 +- sqrt(16)}}}
+2 -4 = -2
+2 +4 = 6
-2 -4 = -6
-2 +4 = 2
{{{0 -sqrt(4) -0 -sqrt(16)}}}
is the correct answer (B)