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Which two numbers is x^2 in between?

Source: AHSME 1963 Problem 40

January 13, 2014
geometry3D geometryAMC

Problem Statement

If xx is a number satisfying the equation x+93−x−93=3\sqrt[3]{x+9}-\sqrt[3]{x-9}=3, then x2x^2 is between:
<spanclass=′latex−bold′>(A)</span> 55 and 65<spanclass=′latex−bold′>(B)</span> 65 and 75<spanclass=′latex−bold′>(C)</span> 75 and 85<spanclass=′latex−bold′>(D)</span> 85 and 95<spanclass=′latex−bold′>(E)</span> 95 and 105<span class='latex-bold'>(A)</span>\ 55\text{ and }65 \qquad <span class='latex-bold'>(B)</span>\ 65\text{ and }75\qquad <span class='latex-bold'>(C)</span>\ 75\text{ and }85 \qquad <span class='latex-bold'>(D)</span>\ 85\text{ and }95 \qquad <span class='latex-bold'>(E)</span>\ 95\text{ and }105
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