Math Problem Statement

Show that a/✔️1+a^2+b/✔️1+b^2+c/✔️1+c^2<3✔️3/2 if 1/ab+1/bc+1/ca=1 through out Jensen

Solution

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Math Problem Analysis

Mathematical Concepts

Inequalities
Concave Functions
Jensen's Inequality

Formulas

f(x) = x / √(1 + x^2)
Jensen's Inequality: f((a + b + c) / 3) ≥ (f(a) + f(b) + f(c)) / 3
Condition: 1/ab + 1/bc + 1/ca = 1

Theorems

Jensen's Inequality

Suitable Grade Level

Undergraduate