Germany Math Olympiad | A Very Nice Algebra Problem | 2 Methods

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[@عبدالواسع-س8م]

Thank you so much !

[@subratabiswas2502]

4×root2=2^2×2^(1/2)=2^(5/2) ; root[2^(5/2)]=2^(5/4) ; 2×2^(5/4)=2^[1+(5/4)]=2^(9/4) ; So, 2^(9/4x)=2^4 ; i,e 9/4x=4 ; i,e 16x=9 ; i,e x=9/16

[@thierrygermain5182]

The index of an arithmetic radical can only be 2, 3, 4, 5...

[@AmirgabYT2185]

x=9/16 but x is a power of root so x≥2 and x∊N, so there are no solutions for x

[@thierrygermain5182]

Absolutely ! As for the method to find x = 9/16, we dream...