Unfortunately, that method could produce extraneous solutions. There is an additional constraint from the original equation that x>=0 since the square root of something must be >=0 (no complex number is a solution, either). That is missing from x^2-x-1=0. Is there a way to make Sage check it with the original equation before displaying the final solutions, or somehow force it to solve the original? Although this may be a simple problem, there are difficult problems with constraints that may be overlooked by someone.
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