lean_workbook_plus_77674

Disproved

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

Let $a,b,c>0$ , and such: $a^2+b^2+c^2=3$ . Prove: $\dfrac{a^4}{\sqrt{b^3+7}}+\dfrac{b^4}{\sqrt{c^3+7}}+\dfrac{c^4}{\sqrt{a^3+7}}\ge \dfrac{3}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_77674 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 ∧ a^2 + b^2 + c^2 = 3 → a^4 / Real.sqrt (b^3 + 7) + b^4 / Real.sqrt (c^3 + 7) + c^4 / Real.sqrt (a^3 + 7) ≥ 3 / 2   :=  by sorry

Source

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

View graph