Hello all!
Once again, I am stuck on a problem, and no matter how I twist it, I always end up in equations that have no solutions.
Question:
The sum of three consecutive members of an arithmetic progression is 2, and the sum of the squares of these members is .
My solution(done with the help of the book's hints)
Let be the "middle" number of the three numbers.
Then
ans if we substitute , we get
But then the equation has no solutions.
All help is appreciated. Anyway, why is it so that some equations do not end up having solutions?