Olympiad Math Trick | Olympiad Challenging Question.

In this tutorial I will lead you on how to solve this kind/type of challenging Olympiad radical equation.
There are some substitutions in solving this mathematical challenge that really need your attention and focus in order for you to be able to grab them I strongly advise you stay glue to this video paying full attention and without skipping any parts of this video.
In solving this challenge, I will teach how to formulate simultaneous equation and even quadratic equation. I will guide you on how to solve all the formed equations step by step.
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Thanks!!!

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[EnriqueCalot]

Awesome video, and awesome problem.

My approach:
if you multiply both sides by x^(1/2) you get

(x^2-1) ^ (1/2) + (x-1) ^ (1/2) = x^(3^2)
and squaring both sides you get

and replacing A=x^3-x^2-x+1 you have A=-1+2A^(1/2) so (A+1)^2 = 4A that is (A-1)^2=0 so A is 1
then 1=x^3-x^2-x+1 so 0 = x^3-x^2-x
since x=0 is not a solution we have 0 = x^2-x-1 that solves to the golden ratio

[chuksnonso]

Well explained prof. But I got a short method to solving this bro.

[ephantuskiondo]

Very lengthy method a shorter method can be used proffessor