x^2+y^2=2a+4
x+y=a+3
find the meaning for "a" when system of equation has only 1 root
please someone help. thanks
(sorry for bad english)
Do you not know how to solve a quadratic equation?
But more to the point, that equation can be written Now, an equation like that will have only one root provided it is a double root. That is, if it is of the form .
-1 should be correct. I get a single solution for the resulting system.
My work disagrees slightly with HallsofIvy, however:
For this quadratic to have a single root, the discriminant must be 0:
Substituting this back into the original equations gives the system
So
A single solution, as desired.