lean_workbook_plus_82846

Proved

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

proofwiki

lower bound :\n\n

\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} >= 1.5

solution\n\n $a=x+y,b=y+z,c=x+z$ \n\n $\sum{\frac{(x+y)^2}{2z(x+y)+(x+y)^2}} >= \sum{\frac{(2x+2y+2z)^2}{2\sum{x^2}+6\sum{ xy}}} >= 3/2$ \n\nthe last step can be proved by $xy+yz+xz <= x^2+y^2+z^2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_82846  (a b c : ℝ)
  (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) :
  a / (b + c) + b / (a + c) + c / (a + b) ≥ 1.5   :=  by sorry

Source

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

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