$\sqrt[4]{2+x}-\sqrt[3]{2-x}=\sqrt[6]{4-x^2}$ find real number $x$. I have tried powering, some substitutions but I couldn't go anywhere. Please help.
2026-04-12 15:12:56.1776006776
Find real number $x$ such that $\sqrt[4]{2+x}-\sqrt[3]{2-x}=\sqrt[6]{4-x^2}$
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HINT: note that $$4-x^2=(2-x)(2+x)$$ p.s.: set $$2-x=a,2+x=b$$ and you will have
$$b^{1/4}=a^{1/6}b^{1/6}+a^{1/3}$$ and $$a+b=4$$