Question

Find the positive difference between the two solutions to the equation rt%5B3%5D%7B4%20-%20%5Cfrac%7Bx%5E2%7D%7B3%7D%7D%20%3D%20-2%20" id="TexFormula1" title=" \displaystyle\sqrt[3]{4 - \frac{x^2}{3}} = -2 " alt=" \displaystyle\sqrt[3]{4 - \frac{x^2}{3}} = -2 " align="absmiddle" class="latex-formula">.
The answer is NOT $0$.

Answer 1

$\displaystyle\sqrt[3]{4 - \frac{x^2}{3}} = -2 \\\\ 4-\dfrac{x^2}{3}=-8\\\\ 12-x^2=-24\\\\ x^2=36\\\\ x=6 \vee x=-6\\\\ 6-(-6)=6+6=12$