Gazeta matematică 2017: Difference between revisions
| Line 6: | Line 6: | ||
<math display="block"> (n+1)ab(a+b)-(4n^3+13n+10)ab+(n+2)^3(a+b) \geq (n+2)^3, </math> | <math display="block"> (n+1)ab(a+b)-(4n^3+13n+10)ab+(n+2)^3(a+b) \geq (n+2)^3, </math> | ||
''oricare ar fi'' <math>a,b \in [1,\infty)</math> | ''oricare ar fi'' <math>a,b \in [1,\infty)</math> | ||
== Gazeta Matematică 9/2017 == | |||
'''[[27429]] (Radu Pop și Vasile Ienutaș, Baia Mare)''' | |||
''Fie <math>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). | |||
</math> | |||
Revision as of 14:35, 23 January 2025
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 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+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). }