Розмір відео: 1280 X 720853 X 480640 X 360
Показувати елементи керування програвачем
Автоматичне відтворення
Автоповтор
161+72√5
@@معلومةفيدقائق-ف9ق thank you... just noticed the mistake at the very last step..
Agree!
63+26=89
(1 + R5)^3 = 1^3 + 3 R5 + 3 (R5)^2 + R5^3 = 1 + 3 R5 + 3 * 5 + 5 R5 = 16 + 8 R5, hence ((1+R5)/2)^3 = 2 + R5.(2+R5)^2 = 4 + 2 * 2 R5 + 5 = 9 + 4R5.(9 + 4R5)^2 = 81 + 9 * 4 * 2 R5 + 16 * 5 = 161 + 72 R5.Not such a nice solution, but only need binomal formulas for squaring and raising to the power 3, which I consider standard for 16 year old high school pupils
@@zaphodbeeblebrox-fz5fh thank you for the observation..
φ = (1+√5)/2φⁿ = F(n)φ + F(n-1), F(n) Fibonacci [proof is trivial by induction]φ¹²=F(12)φ + F(11) = 144φ + 89 = 161 + 72√5
@@HakimsChannel thank you!
161+72√5
@@معلومةفيدقائق-ف9ق thank you... just noticed the mistake at the very last step..
Agree!
63+26=89
(1 + R5)^3 = 1^3 + 3 R5 + 3 (R5)^2 + R5^3 = 1 + 3 R5 + 3 * 5 + 5 R5 = 16 + 8 R5, hence ((1+R5)/2)^3 = 2 + R5.
(2+R5)^2 = 4 + 2 * 2 R5 + 5 = 9 + 4R5.
(9 + 4R5)^2 = 81 + 9 * 4 * 2 R5 + 16 * 5 = 161 + 72 R5.
Not such a nice solution, but only need binomal formulas for squaring and raising to the power 3, which I consider standard for 16 year old high school pupils
@@zaphodbeeblebrox-fz5fh thank you for the observation..
φ = (1+√5)/2
φⁿ = F(n)φ + F(n-1), F(n) Fibonacci [proof is trivial by induction]
φ¹²=F(12)φ + F(11) = 144φ + 89 = 161 + 72√5
@@HakimsChannel thank you!