lean_workbook_plus_75641

Proved

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

Let $a,b,c$ be positive real numbers such that $abc=1$ . Prove that $\frac{1}{a^2-a+1} \leqslant \frac{3}{2} \cdot \frac{a^2+1}{a^4+a^2+1}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_75641 (a b c : ℝ) (h : a * b * c = 1) :
  (1 / (a ^ 2 - a + 1)) ≤ (3 / 2) * (a ^ 2 + 1) / (a ^ 4 + a ^ 2 + 1)   :=  by sorry

Source

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

View graph