lean_workbook_plus_62514

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 \n $$\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_62514 (a b c : ℝ) (habc : 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

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