A Multi-Valued Radical Parametrization for Chebyshev-Type Polynomial Equations via Algebraic Inversion

This work presents a structured algebraic parametrization of solutions to Chebyshev-type polynomial equations, offering an alternative to trigonometric inversion. The method applies to equations of the form P_n(y) = C where P_n(y) = 2T_n(y/2), and provides a multi-valued radical expression that yields a real root under appropriate branch selection. The sextic case is treated in detail, and the generalization to arbitrary degree n is established. This is a preprint that has not yet undergone peer review.