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
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Prove Inequality Using Jensen's Inequality with ab + bc + ca = 1
Proving Inequality with Jensen’s Inequality for a, b, and c
Proving Inequality Using Jensen's and AM-GM Inequalities with a + b + c = 1
Proving Inequality Involving AM-GM: a, b, c > 0 with a + b + c = 3
Inequality Proof: a^3/(a^2 + b^2) + b^3/(b^2 + c^2) + c^3/(c^2 + a^2) ≥ 1/2