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

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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## 14 Replies to “Math Olympiad Question | Golden Ratio: a^12=? | Math Olympiad Preparation”

1. 이호석 says:

sir your solutions amaze me always

2. John Alcaraz says:

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.

3. Kevin Silva says:

Amazing! Another application of the Chain Rule of substitutions. Tricky but effective.

4. Jayant Sahay says:

Ans : 161 + 72_/5

5. 242 MATH says:

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

6. Pankaj Singh says:

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

7. angshuk nag says:

Value can be found by using fibonacci recurrence

8. Ольга Соломашенко says:

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

9. Nico Gehren says:

very nice question

10. Tambuwal Maths Class says:

Nice technique

11. J. R. says:

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.

12. HIDY says:

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

13. Ramani Venkata says:

Classic explanation

14. Mustafiz Rahman says:

It was really good question.