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1968 AMC 12 #28 - Arithmetic Mean

Source:

January 1, 2012
ratioquadraticsalgebraAMC

Problem Statement

If the arithmetic mean of aa and bb is double their geometric mean, with a>b>0a>b>0, then a possible value for the ratio ab\frac{a}{b}, to the nearest integer, is
<spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 8<spanclass=′latex−bold′>(C)</span> 11<spanclass=′latex−bold′>(D)</span> 14<spanclass=′latex−bold′>(E)</span> none of these<span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 8 \qquad<span class='latex-bold'>(C)</span>\ 11 \qquad<span class='latex-bold'>(D)</span>\ 14 \qquad<span class='latex-bold'>(E)</span>\ \text{none of these}
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