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Consider the following system of inequalities:

{ 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 -

    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 -

    ohw... sorry for that... for clarification, it's:

    { cx^2 + 2(c+1)x+(c+1)>or=0

  • algebra -

    5/4. Giving 9

  • algebra -

    no, its incorrect

  • algebra -

    19 is the correct answer

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