Math Olympiad | A Beautiful Exponential Problem | VIJAY Maths

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[@flaviobsyou]

Very nice!

[@vijaymaths5483]

Thank you! Cheers!

[@andryvokubadra2644]

[(1+√5)/2]¹² = ?
=============
[(1+√5)/2]² = ¼(1+2√5+5)
[(1+√5)/2]² = ¼(6+2√5)
[(1+√5)/2]² = ½(3+√5)
[(1+√5)/2]⁴ = [½(3+√5)]²
[(1+√5)/2]⁴ = ¼(9+6√5+5)
[(1+√5)/2]⁴ = ¼(14+6√5)
[(1+√5)/2]⁴ = ½(7+3√5)
[(1+√5)/2]^8 = [½(7+3√5)]²
[(1+√5)/2]^8 = ¼(49+42√5+45)
[(1+√5)/2]^8 = ¼(94+42√5)
[(1+√5)/2]^8 = ½(47+21√5)
[(1+√5)/2]¹² = [(1+√5)/2]⁴ * [(1+√5)/2]^8
[(1+√5)/2]¹² = ½(7+3√5) * ½(47+21√5)
[(1+√5)/2]¹² = ¼(7*47+3*47√5+7*21√5+3*21*√5*√5)
[(1+√5)/2]¹² = ¼(329 + 288√5 + 315)
[(1+√5)/2]¹² = ¼(644+288√5)
[(1+√5)/2]¹² = 161 + 72√5
161 + 72√5 = 322 9:43