Gazeta matematică 2017

Gazeta Matematică 6-7-8/2017

27401 (Radu Pop)

Fie Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n \in \mathbb{N}} . Să se arate că

$$(n+1)ab(a+b)-(4n^{3}+13n+10)ab+(n+2)^{3}(a+b)\geq (n+2)^{3},$$

oricare ar fi Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a,b \in [1,\infty)}

Gazeta Matematică 9/2017

27429 (Radu Pop și Vasile Ienutaș, Baia Mare)

Fie Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A, B \in M_3(\mathbb{R})<math> cu proprietatea că <math>A^2 + B^2 = 2AB + BA<math>. Să se arate că'' <math> \det(4AB - BA) + \det(AB - 4BA) = 10\det(AB + 2BA) - 10\det(2AB + BA). }