lean_workbook_plus_9084

Proved

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

Let $a,b,c$ be non negative real numbers satisfying $a+b^2+c^2=1$ . Prove that $(1+a^2)(1+b^2)(1+c^2)\geq \frac{50}{27}$ Equality holds when $a=\frac{1}{3},b=0,c=\sqrt{\frac{2}{3}}$ or $a=\frac{1}{3},b=\sqrt{\frac{2}{3}},c=0.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9084 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b^2 + c^2 = 1) : (1 + a^2) * (1 + b^2) * (1 + c^2) ≥ 50 / 27 ∧ (a = 1 / 3 ∧ b = 0 ∧ c = Real.sqrt (2 / 3) ∨ a = 1 / 3 ∧ b = Real.sqrt (2 / 3) ∧ c = 0) ↔ a = 1 / 3 ∧ b = 0 ∧ c = Real.sqrt (2 / 3) ∨ a = 1 / 3 ∧ b = Real.sqrt (2 / 3) ∧ c = 0   :=  by sorry

Source

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

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