Let p,q,and r be real numbers so that p+q+r = 2 and p2+q2+r2 = 12
Then, the sum of the maximum and minimum value of r is
The Attempt at a Solution
p+q+r = 2
p^2+q^2+r^2 + 2 (pq+qr+pr) = 4
12 + 2 (pq+qr+pr) = 4
pq+qr+pr = -4
I think I should determine the value of pqr so that I can treat p,q,r as roots of a polynomial.
But, I have no idea about it.