Germany | Can you solve this? | Math Olympiad Problem

[@johnmaulkin-ur8lm]

Very clever, thank you.

[@arumairajputhirasigamani2907]

Direct expansion is more simpler.. x = (√3-1)/2 x^2 = (3+1-2√3)/4 = 1- √3/2 x^4 = (1-√3/2)^2 = 1 + 3/4 - √3 = 7/4 - √3 x^8= (7/4 - √3)^2 = 49/16 + 3 -7√3/2 = 97/16 - 7√3/2 x^8 * x^2 = x^10 = (97/16 - 7√3/2) * (1 - √3/2) x^10 = 97/16 - 7√3/2 - 97√3/32 + 21/4 = 181/16 - 209√3/32

[@michaeledwards2251]

I was thinking similarly. Take (1/2)^10 as (1/1024), I know 2^10 by heart. And expand (root(3) - 1)^10 using powers of 2, 4 and 8, to generate power of 10 and divide by 1024. For my generation who learned how to calculate do to no calculators being available, I was born in 1953, definitely the easiest method. The problem today is the typical student struggles with arithmetic.

[@riccardovascon5041]

Congratulations