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## Homework Statement

Let p,q,and r be real numbers so that p+q+r = 2 and p

^{2}+q

^{2}+r

^{2}= 12

Then, the sum of the maximum and minimum value of r is

A. 4/3

B. 2

C. 3

D. 10/3

E. 4

## Homework Equations

basic algebra

## The Attempt at a Solution

[/B]

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.

Please help

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