MathDB
Minimizing y

Source: 1964 AHSME Problem 24

August 23, 2013
conicsparabolaAMC

Problem Statement

Let y=(x−a)2+(x−b)2,a,by=(x-a)^2+(x-b)^2, a, b constants. For what value of xx is yy a minimum?
<spanclass=′latex−bold′>(A)</span> a+b2<spanclass=′latex−bold′>(B)</span> a+b<spanclass=′latex−bold′>(C)</span> ab<spanclass=′latex−bold′>(D)</span> a2+b22<spanclass=′latex−bold′>(E)</span> a+b2ab <span class='latex-bold'>(A)</span>\ \frac{a+b}{2} \qquad<span class='latex-bold'>(B)</span>\ a+b \qquad<span class='latex-bold'>(C)</span>\ \sqrt{ab} \qquad<span class='latex-bold'>(D)</span>\ \sqrt{\frac{a^2+b^2}{2}}\qquad<span class='latex-bold'>(E)</span>\ \frac{a+b}{2ab}
Back to ProblemsView on AoPS