lean_workbook_plus_54255

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove the inequality with Jensen's inequality: \n $x,y,z$ are Positive Real, prove that: \n

\frac{x^2}{x+y}+\frac{y^2}{y+z}+\frac{z^2}{z+x}\ge\frac{x+y+z}{2}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_54255 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x^2 / (x + y) + y^2 / (y + z) + z^2 / (z + x)) ≥ (x + y + z) / 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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