Can you solve the given math olympiad rational question involving radicals and exponents?

Find the value of a^12 in this Golden Ration problem.

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Math Olympiad Question | Golden Ratio: a^12=? | Math Olympiad Preparation

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Golden Ratio

Golden Ratios

a^12=?

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sir your solutions amaze me always

And if a=(1-√5)/2, then a^12=161-72√5. Both a=(1+√5)/2 and a=(1-√5)/2 are solutions to the quadratic equation a^2=a+1. Once you derive the result a^12=144a+89, you can plug in either value of a on the right-hand side of the equation to get the value of a^12.

Amazing! Another application of the

Chain Ruleof substitutions. Tricky but effective.Ans : 161 + 72_/5

very well done, thanks for sharing the solution to this Golden Ratio problem

It is easy if you simply do Cube then Square & then square we get results 2+root5 then 9+4×root5 then 161+72×root5

Value can be found by using fibonacci recurrence

Square the expression, then square it again, then cube it.

very nice question

Nice technique

I'm not sure that it's any easier to proceed in this way than to simply work with the right-hand side of the original equation. The fact that a radical is present doesn't make it hard in this case. First I calculated the square of the right side, then the cube. Then I just squared that result twice to get ^6 and ^12. The correct answer popped out neatly at the end.

Можно было заметить что каждая степень этого уравнения есть ряд Фибоначчи и тогда не надо таких огромных вычеслений

Classic explanation

It was really good question.