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Question Number 164650 by cortano1 last updated on 20/Jan/22

$$\sqrt[3]{x+9}-\sqrt[3]{x-9}=3$$$$x=?$$

Answered by mr W last updated on 20/Jan/22

$${(\sqrt[3]{9+x}+\sqrt[3]{9-x})}^3=3^3$$$$(9+x)+(9-x)+3\times 3\sqrt[3]{9^2-x^2}=27$$$$\sqrt[3]{9^2-x^2}=1$$$$9^2-x^2=1$$$$x^2=80$$$$x=\pm \sqrt{80}=\pm 4\sqrt{5}$$

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