MODERN METHODS OF PROOF OF INEQUALITIES

Arslanova Nodira Ikromjon Qizi

Arslanova Nodira Ikromjon Qizi 3-year student of Kokand state pedagogical institute in Fergana region in Republic of Uzbekistan

Keywords: Inequalities, sum of reciprocal inverse numbers, introduction of new variables, real numbers, positive numbers, methods, square.

Abstract

The article presents new effective methods of proving inequalities and problems in various mathematical Olympiads on their application. The manual is intended for gifted students of general secondary schools, academic lyceums and vocational colleges, teachers of mathematics and students of pedagogical universities. One of the basic procedures for proving inequalities is to rewrite them as a sum of squares and then according to the most elementary property that the square of real number is non negative to prove a certain inequality

References

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 Kim Hung, P: “Secrets in Inequalities”, Gil publishing House (2007).
 Andreescu, T., Enescu, B.: Mathematical Olympiad Treasures. Birkhäuser, Basel (2003)
 Andreescu, T., Cirtoaje, V., Dospinescu, G., Lascu, M. : Old and New Inequalities. Gil Publishing House, Zalau (2004)