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HKIMO 2020 THPT (Grades 10–12 shared) National Final (Heat) Set 01 Question 14

HKIMO · HKIMO 2020 THPT (Grades 10–12 shared) National Final (Heat) Set 01

Question 14

Given $x\gt 0$ and $x=32\sqrt{4\sqrt{32\sqrt{4\sqrt{\cdots}}}}$, find $x$.