Q10 of SMO 2019 Senior (Geometry and algebra.Minimum length)

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Singapore Mathematical Olympiad (SMO) Senior 2019.

We are asked to find the minimum value of an expression, which regularly can be solved using Calculus. However, we applied AM-GM inequality instead. Check it out! This question is suitable for beginners.

SMO Senior 2019 paper can be found here:

Check it out and have fun!
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if X = (9)^1/3 +(3)^1/3 + 1
find the valu of [(X+2)/2]^12

shivkumarchoudhary