Abstract ▼ AI-Helper

The relation between arithmetic mean and qeotnetric mean in two variables plays an important role in applicationsw one of which is the problem to solve the (relative) maxima and the (relative) minima of the product of two real numbers or two real-valued functions y and to prove the inequalities in s...

The relation between arithmetic mean and qeotnetric mean in two variables plays an important role in applicationsw one of which is the problem to solve the (relative) maxima and the (relative) minima of the product of two real numbers or two real-valued functions y and to prove the inequalities in secondary school course. In this note we investigate the historical process of the relations between arithmetic mean and geometric mean in orde to contribute to the research of educational materials. an give several proofs of the general relation between arithm mean and geometric mean in n variables, i.e. a_1+ a_2 +... + a_n/n ≥ n√a_1a_2...a_n where a_1, a_2,... ,a_n are positve numbers.