A weighted quadratic inequality

Proved

WorkbookSource.problem_722

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

lean-workbooksource-checked

By AM-GM, $16x^2+25y^2+36z^2=\frac{45}{2}(y^2+z^2)+\frac{27}{2}(z^2+x^2)+\frac{5}{2}(x^2+y^2)\ge 45yz+27xz+5xy .$

Source: InternLM Lean-Workbook, record lean_workbook_722 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_722 : ∀ x y z : ℝ, 16 * x ^ 2 + 25 * y ^ 2 + 36 * z ^ 2 ≥ 45 * y * z + 27 * z * x + 5 * x * y  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_722; Apache-2.0

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