A cubic inequality on the nonnegative reals

Proved

WorkbookSource.problem_55336

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

lean-workbooksource-checked

Prove that $x^3+15x\ge 7x^2$ for all $x\ge 0$ .

Source: InternLM Lean-Workbook, record lean_workbook_55336 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_55336 (x : ℝ) (hx : 0 ≤ x) : x ^ 3 + 15 * x ≥ 7 * x ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_55336; Apache-2.0

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