A nice mathematics algebra exponential rational problem | Olympiad Question| x=?

[@MuhammadAwais-uf7cg]

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[@HuzaifaKhan-m3i]

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[@souzasilva5471]

Eudivide cada termo por 6x. fiz x/6-1/x= a. e cheguei a [sqrt(2) - sqrt(26)]/2 ou x = [-sqrt(2)+-sqrt(26)]/2. Se for uma questão de múltipla escolha, a gente fica sema saber. No entato minhas respostas são as mesmas que as suas, porém expressas de maneiras diferentes.(I divide each term by 6x. I did x/6-1/x= a. and I arrived at [sqrt(2) - sqrt(26)]/2 or x = [-sqrt(2)+-sqrt(26)]/2. If it's a multiple choice question, we don't know. However, my answers are the same as yours, but expressed in different ways.) I await your comment. Grateful.

[@dan-florinchereches4892]

If a=(x^2-6)/6x the the equation becomes (a-1/6)^2+(a+1/6)^2=1/6 2a^2+2/36=1/6 a^2=2/36 a=+-√2/6 I a=√2/6 => x^2-6=√2x X1,2=(√2+-√(4+4*6))/2=(√2+-2√7)/2 When a=-√2/6we get X3,4=(-√2+-2√7)/2

[@turhan70]

To many unnecessary intermediate steps.

[@NaeemKhan-n7j]

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