A product-square inequality

Proved

WorkbookSource.problem_53827

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that $a^{4}+b^{2}c^{2}\geq 2a^{2}bc$ for all $a,b,c \in R$

Source: InternLM Lean-Workbook, record lean_workbook_53827 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_53827 (a b c : ℝ) : a ^ 4 + b ^ 2 * c ^ 2 ≥ 2 * a ^ 2 * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_53827; Apache-2.0

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