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In mathematics, the Newton inequalities are named after Isaac Newton. Suppose a 1, a 2, ..., a n are non-negative real numbers and let denote the kth elementary symmetric polynomial in a 1, a 2, ..., a n. Then the elementary symmetric means, given by = (),
Similar to equation solving, inequation solving means finding what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an inequation or a conjunction of several inequations. These expressions contain one or more unknowns, which are free variables for which values are sought that cause the condition to be fulfilled ...
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);
Askey–Gasper inequality; Babenko–Beckner inequality; Bernoulli's inequality; Bernstein's inequality (mathematical analysis) Bessel's inequality; Bihari–LaSalle inequality; Bohnenblust–Hille inequality; Borell–Brascamp–Lieb inequality; Brezis–Gallouet inequality; Carleman's inequality; Chebyshev–Markov–Stieltjes inequalities ...
For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 .
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