Hong Kong l A Beautiful Exponential Problem l Math Olympiad

[@touratiaziz5059]

رائع شكرا

[@wes9627]

A Golden Ratio problem to feast on. Let Φ=(√5+1)/2 represent the Golden Ratio and φ=1/Φ=(√5-1)/2 its inverse. Then Φ^3=2Φ+1=√5+2 and φ^3=2φ-1=√5-2. Thus, ∛(√5+2)+∛(√5-2)=Φ+φ=(√5+1)/2+(√5-1)/2=√5 and [∛(√5+2)+∛(√5-2)]^2024=[Φ+φ]^2024=√5^2024=5^1012,

[@raghvendrasingh1289]

❤ also cube root (√5+2) - cube root (√5 - 2) = 1

[@Danieswors]

5^1012

[@RealQinnMalloryu4]

(1 2^3 +1.+1^2^3 ➖ 1)^100^200^24 (1^1+ 1^1)^1^2^2^12 ()^1^1^2^6 ()^1^2^2^3 ()^1^1^2^3 ()^2^3(x ➖ 3x+2).