Asked by hmmm
Consider the following system of inequalities:
{(c-1)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.
{(c-1)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.
Answers
Answered by
Steve
You sure these are < and >, not <= and >=?
Solutions to such are open intervals.
Intersections of open intervals cannot be a single value for x.
Solutions to such are open intervals.
Intersections of open intervals cannot be a single value for x.
Answered by
hmmm
ohw... sorry for that... for clarification, it's:
{(c-1)x^2+2cx+c+4<or=0
{ cx^2 + 2(c+1)x+(c+1)>or=0
{(c-1)x^2+2cx+c+4<or=0
{ cx^2 + 2(c+1)x+(c+1)>or=0
Answered by
pi
5/4. Giving 9
Answered by
Math defender
no, its incorrect
Answered by
hans
19 is the correct answer
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.