A tricky problem with divine answer | Math Olympiad Problem

[@nicogehren6566]

very nice question

[@faysal...]

Keep uploading harder ones mate... Keep it up

[@elearn1]

Təbtik edirəm.

[@elearn1]

Ugurlar arzulayiram

[@t.sambath]

Good ❤🎉

[@hristoistoyanov]

Ok, i am too lazy to try it, but .... What if you go the "naive" way: Just raise to 2 both sides of fhe original equation and go from there...?

[@emmanuellaurens2132]

Square both side, one square root remains from the cross-multiplication on the left side. Put everything else on the other side, square again, and you now have a 4th degree polynomial to solve (thankfully the 1/x and 1/x² cancel). I even worked it out and here it is: x^4 - 2 x^3 - x² +2x +1 = 0 Now, this does factor as (x² - x -1)² = 0, and we're back on track for the solution, but that factorization is not easy to see unless you already know where you are going :/ The palindrome in the coefficient is an hint, but not much of one.

[@mrgold4678]

Are you kidding man… There are many mistakes in your solution. When you are multiplying both sides by (a - b) you should check whether it is zero. Also when you have found x you should check it by putting it into the original equation (cause there could be some issues with b < 0 etc)

[@SolveWithMT]

Firstly, no need to focus on checking whether (a-b) is equal to 0, because if it is, then a = b, that is x - 1/x = 1 - 1/x. This in turn means that x = 1, but if we put this value into the original equation, we will get 0 = 1, which is obviously wrong Secondly, it is too obvious for me to put the value of x into the original equation there (1.618 > 1, so 1/618 < 1, and that means b is positive)

[@jyl123]

bro got destroyed by facts and logic

[@anitm5313]

@@jyl123Who got destroyed?