Olympiad Mathematics | Learn to find the value of (2^9x)+1/(2^9x) | Math Olympiad Preparation

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Olympiad Mathematics | Learn to find the value of (2^9x)+1/(2^9x) | Math Olympiad Preparation

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[johnbrennan]

2^9x +1/ (2^ 9x) can be written as (2^3x)^3 + 1\( 2^3x)^3. That is the sum of two cubes so factorize. 8^x +1\ ( 8^x) can be written as 2^3x +1\(2^ 3x). End up with702

[johnwindisch]

Learning to use those polynomial identities!!
Thank you

[kanankazimzada]

Indeed, this solution is incredible. Nice to understand this solution

[luisalfredonarvaeznarvaez]

Es formidable la destreza de solucionar estos tipos de ejercicios aplicando los productos notables
Gracias Profesor
Saludos y Bendiciones desde Nicaragua

[owlsmath]

Nice problem! I did it by substitution u = 8^x.

[predator]

As always excellent explanation and very nice solution👍. Thank you teacher 🙏.

[ravikumargautam]

Wow! This is a tricky and easy question.

[fabatcazityt]

Thanks for this stimulating equation thanks Mr pre math you are the best mathimatique teacher in the World thanks 🔥🔥🧑‍🏫🧑‍🏫🧑‍🏫😘😘😘😃😃😄😄😀😀😀😀🥰🥰🥰✨✨

[div]

EASY, EVEN I SOLVED IT FAST. YOUR SOL. IS SAME AS MINE😉

[millaarsenal]

It's simple problem! But
I found two answers 702 and 0.0014

[indianbhai]

Easy problem but interesting
Thanks sir🙏🙏🙏

[Jack_Callcott_AU]

I did the problem in a very strange way, but, unfortunately, I had to use a calculator.
I said cosh(x*ln(8)) = 9/2, which I derived from the first equation, then from the second equation we have to find 2*cosh(9*x*ln(2)) = 2*cosh(3*x*ln(8)) since ln(8)=3*ln(2), then I had to use a calculator to get 702.0000.