Software
The arithmetic-geometric mean inequality (I)
Autor
Rosa, Félix Martínez de la
Martínez, Soledad Mª Sáez
Resumen
The arithmetic-geometric mean inequality: √ab ≤ (a+b)/2, for a,b ≥ 0.
The figure shows that (a+b)²-(a-b)²=4ab, therefore √ab = √[(a+b)²-(a-b)²]/4 ≤ √[(a+b)²]/4 = (a+b)/2 Ensino Médio::Matemática