Math Olympiad | A Nice Math Olympiad Problem | Solving Exponential Equations

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[hvok]

Wow, so clean. A pattern in your last few videos have been rearanging, factoring out, and creating substitutions inorder to find a quadratic factor. I appreciate these examples.

[bvideoz]

t = 2^x
t+t²=t³
t³-t²-t=0
t(t²-t-1) = 0
At this point I feel really bored to continue 🤪
Obviously t=0 makes no sense as there is no such a power for 2 to yield 0, solving this innocently looking quadratic equation will get us the roots - by looks of it irrational ones (hence I can't be bothered to find them)

[IAmRogerXi]

kudos to the very detailed explanation.👍 however, this is not a hard problem. 😀

[BigParadox]

Here is my similar solution which you can view in nice mathematical notation if you go to the Tiny URL link having the code yc5aj54r
It involves completing the square when it comes to solving the quadratic.