Løsningssum

Løsningssum is a Norwegian term that translates to "solution sum" or "sum of solutions." It typically refers to the sum of all valid solutions to a mathematical equation or problem. This concept is often encountered in areas like algebra, where one might be asked to find the sum of the roots of a polynomial. For example, if a quadratic equation has solutions $x_1$ and $x_2$, the løsningssum would be $x_1 + x_2$. Similarly, in problems involving multiple conditions or constraints, the løsningssum would be the sum of all values or combinations that satisfy all the given criteria. The term is not specific to any particular mathematical field and can be applied broadly wherever a set of solutions needs to be aggregated by summation. Understanding the løsningssum is crucial for fully characterizing the complete answer set of a problem. It can sometimes be determined directly without finding each individual solution, such as through Vieta's formulas for polynomials.