lean_workbook_plus_3633

Proved

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

Find: $a^2(b+c) + b^2(a+c) + c^2(a+b)$ if $a+b+c=6$ , $a^2+b^2+c^2=40$ , and $a^3+b^3+c^3=200$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_3633 (a b c : ℝ) (h₁ : a + b + c = 6) (h₂ : a ^ 2 + b ^ 2 + c ^ 2 = 40) (h₃ : a ^ 3 + b ^ 3 + c ^ 3 = 200) : a ^ 2 * (b + c) + b ^ 2 * (a + c) + c ^ 2 * (a + b) = 40   :=  by sorry

Source

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

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