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.

Today I will teach you tips and tricks to solve the given olympiad math question in a simple and easy way. Learn how to prepare for Math Olympiad fast!
Step-by-step tutorial by

Need help with solving this Math Olympiad Question? You’re in the right place!

I have over 20 years of experience teaching Mathematics at American schools, colleges, and universities. Learn more about me at

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

Olympiad Mathematical Question! | Learn Tips how to solve Olympiad Question without hassle and anxiety!

#OlympiadMathematicalQuestion #HowToSolveOlympiadQuestion #MathOlympiadQuestion #MathOlympiadQuestions #OlympiadQuestion #Olympiad #AlgebraReview #Algebra #Mathematics #Math #Maths
#MathOlympiadPreparation #LearntipstosolveOlympiadMathQuestionfast #OlympiadMathematicsCompetition #MathOlympics #SolveSystemofEquations
#HowToThinkOutsideTheBox #ThinkOutsideTheBox #HowToThinkOutsideTheBox?
#RadicalEquations #RationalEquations #ExponentialEquations #MathOlympics #blackpenredpen #OlympiadMathematics #GoldenRatio #GoldenRatios

Golden Ratio
Golden Ratios
How to solve Olympiad Mathematical Question
How to prepare for Math Olympiad
How to Solve Olympiad Question
How to think outside the box?
How to Solve international math olympiad questions
international math olympiad questions and solutions
international math olympiad questions and answers
olympiad mathematics competition
math olympics
olympiad exam
olympiad exam sample papers
math olympiad sample questions
math olympiada
British Math Olympiad
olympics math
olympics mathematics
olympics math activities
olympics math competition
Math Olympiad Training
How to win the International Math Olympiad | Po-Shen Loh and Lex Fridman
Po-Shen Loh and Lex Fridman
Number Theory
There is a ridiculously easy way to solve this Olympiad qualifier problem
This U.S. Olympiad Coach Has a Unique Approach to Math
The Map of Mathematics
math at work
exponential equation
system of equations
solve system of equations
solve the equation
Math puzzles
pre math
Po Shen Loh
Olympiad Mathematics

Subscribe Now as the ultimate shots of Math doses are on their way to fill your minds with the knowledge and wisdom once again.

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

  1. 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.

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

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

  4. 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

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

  6. 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.

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

Comments are closed.