The discussion revolves around solving an equation involving surds, specifically the equation ##x^{1/6}=12x^{1/3}-1##. Participants explore algebraic and numerical methods for finding solutions, questioning the validity of substitutions and transformations applied to the equation.
The discussion is active, with participants offering insights into the algebraic structure of the problem and exploring different approaches. Some participants have identified potential solutions, while others emphasize the importance of checking these solutions against the original equation. There is a recognition of the complexity of similar problems involving surds.
Participants note that certain equations may not yield rational or integer solutions, and there is an ongoing exploration of the limits of algebraic methods for higher-degree equations. The discussion also touches on the need for numerical methods in cases where closed-form solutions are not feasible.
sorry for not seeing then, ...##u=2##fresh_42 said:Yes, and ##12=12\cdot 1 = 6 \cdot 2 = 4 \cdot 3##. Which one do we get for ##u##?