Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus
During AMC testing, the AoPS Wiki is in read-only mode and no edits can be made.

2013 AMC 12B Problems/Problem 17

Revision as of 14:58, 22 February 2013 by Zverevab (talk | contribs) (Created page with "==Problem== Let <math>a,b,</math> and <math>c</math> be real numbers such that <math>a+b+c=2,</math> and <math> a^2+b^2+c^2=12 </math> What is the difference between the max...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $a,b,$ and $c$ be real numbers such that $a+b+c=2,$ and $a^2+b^2+c^2=12$

What is the difference between the maximum and minimum possible values of $c$?

$\text{(A) }2\qquad \text{ (B) }\frac{10}{3}\qquad \text{ (C) }4 \qquad \text{ (D) }\frac{16}{3}\qquad \text{ (E) }\frac{20}{3}$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2013_AMC_12B_Problems/Problem_17&oldid=51371"