Math Olympiad Question | Solve the value of f(3), given that f(x+1x) = x^5 + 1/x^5 | Algebra

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Math Olympiad Question | Solve the value of f(3), given that f(x+1x) = x^5 + 1/x^5 | Algebra Challenge

[wannabeactuary]

x +1/x = 3 implies x^2 -3x + 1 = 0
implies (x -1.5)^2 - 1.25 =0 implies x - 1.5 = +/- sqrt(5/4) = +/- sqrt(5)/2
implies x = 1.5 + sqrt(5)/2 = (3 +sqrt(5))/2
or x = 1.5 - sqrt(5)/2 = (3 - sqrt(5))/2

now I am stuck