A quadratic sum is bounded by a reciprocal sum at fixed sum three

Proved

WorkbookSource.base_21324

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers such that $a+b+c=3$ . Prove : $10\Big(a^2+b^2+c^2\Big)-8\Bigg(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\Bigg)\le9$

Source: InternLM Lean-Workbook, record lean_workbook_21324 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_21324 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (hab : a + b + c = 3) : 10 * (a ^ 2 + b ^ 2 + c ^ 2) - 8 * (1 / a + 1 / b + 1 / c) ≤ 9  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21324; Apache-2.0

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