lean_workbook_plus_32594

Proved

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

Let $a,b$ are real numbers and satisfy $0<b<a \leq 4$ and $2 a b \leq 3 a+4 b$ . Prove that

a^{2}+b^{2}\leq 25

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_32594 (a b : ℝ) (h₁ : 0 < b ∧ b < a ∧ a ≤ 4) (h₂ : 2 * a * b ≤ 3 * a + 4 * b) : a^2 + b^2 ≤ 25   :=  by sorry

Source