<s>[INST] If:$(\sqrt{x + 9})^{\frac{1}{3}} - (\sqrt{x-9})^{\frac{1}{3}} = 3$, Find $x^2$ 

If:$$\sqrt[3]{(x + 9)} - \sqrt[3]{(x-9)} = 3$$
    Find $x^2$


I can't seem to solve this question. Any hints or solutions is welcomed.
 [/INST] Put $a=(x+9)^{1/3},b=(x-9)^{1/3}$
$$a-b=3\\(a-b)^3=3^3\\a^3-3ab(a-b)+b^3=27$$
Now you already know that $a-b=3$ so
$$a^3-9ab-b^3=27$$
Now plugging back $a,b$
$$((x+9)^{1/3})^3-9(x+9)^{1/3}(x-9)^{1/3}-((x-9)^{1/3})^3=27\\x+9-9(x^2-81)^{1/3}-(x-9)=27\\18-9(x^2-81)^{1/3}=27\\(x^2-81)^{1/3}=-1\\x^2-81=-1\\x^2=80$$
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