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.
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.
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?