lean_workbook_plus_40593

Proved

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

for $x,y,a,b>0$ one has $\dfrac {x^2} {a} + \dfrac {y^2} {b} \geq \dfrac {(x+y)^2} {a+b}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_40593 (x y a b : ℝ) (hx : 0 < x) (hy : 0 < y) (ha : 0 < a) (hb : 0 < b) : (x ^ 2 / a + y ^ 2 / b) ≥ (x + y) ^ 2 / (a + b)   :=  by sorry

Source

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

View graph