megoldóképlet

Megoldóképlet is a term used in Hungarian mathematics to describe a formula or closed‑form expression that directly yields the solution to a problem from the given data, without the need for iterative procedures. It is most commonly applied to algebraic problems, such as solving equations or determining unknowns, and to linear systems where a single expression provides the answer. The concept emphasizes a direct computation rather than an algorithmic or numerical process.

A classical example is the solution of a quadratic equation ax^2 + bx + c = 0 with a ≠ 0, where the solutions are x = (-b ± sqrt(b^2 − 4ac)) / (2a). The quantity b^2 − 4ac is the discriminant and determines the nature of the roots. Another widely cited megoldóképlet is Cramer's rule for a linear system, which expresses each variable as a ratio of determinants: x = Δx/Δ, y = Δy/Δ, where Δ is the determinant of the coefficient matrix and Δx, Δy are determinants formed by replacing corresponding columns with the constants.

The notion also covers other formulas used to obtain solutions directly, such as certain geometric or arithmetic formulas, where a single expression yields the desired quantity from given inputs. However, megoldóképletek have limitations: not every problem admits a formula in radicals or in simple closed form. For example, the general quintic has no formula in radicals, and some formulas exist only in more advanced or complex forms.

In education and mathematics discourse, megoldóképlet is a useful concept to illustrate how problems can be solved in one step from data, highlighting structure and relationships rather than relying solely on iterative methods.