Posted by hmmm on Monday, April 29, 2013 at 11:46am.
Consider the following system of inequalities:
{(c1)x^2+2cx+c+4<0
{ cx^2 + 2(c+1)x+(c+1)>0
The sum of all real values of c, such that the system has a unique solution, can be written as ab, where a and b are coprime positive integers. What is the value of a+b?
Details and assumptions
c can be negative.
The system has a unique solution if there is only 1 real value x which is satisfied throughout.

algebra  Steve, Monday, April 29, 2013 at 2:32pm
You sure these are < and >, not <= and >=?
Solutions to such are open intervals.
Intersections of open intervals cannot be a single value for x. 
algebra  hmmm, Tuesday, April 30, 2013 at 2:35am
ohw... sorry for that... for clarification, it's:
{(c1)x^2+2cx+c+4<or=0
{ cx^2 + 2(c+1)x+(c+1)>or=0 
algebra  pi, Wednesday, May 1, 2013 at 6:50am
5/4. Giving 9

algebra  Math defender, Thursday, May 2, 2013 at 11:35am
no, its incorrect

algebra  hans, Tuesday, May 7, 2013 at 1:41am
19 is the correct answer