Gazeta matematică 2024: Difference between revisions

Revision as of 07:39, 4 August 2025

Gazeta Matematică 5/2024

P:1791 (Vraja-Lőkös Éva-Ibolya)

Suma a două numere naturale, pare, consecutive este 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 90} . Aflați produsul acestor numere.

28868 (Andre Horvat-Marc)

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^\ast}} și funcțiile $f:\left[0,2n^{2}+3n\right]\to \left[1,2n+1\right]$ , 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 f\left(x\right) = \frac{\sqrt{8x+9}-1}{2}}

și 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  g:\left[1,2n+1\right] \to \left[0,2n^2+3n\right]}
, 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  g\left(x\right) = f^{-1}\left(x\right)}
.Fie punctele 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\left(2n^2+3n,2n+1\right)}
, 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 B\left(2n+1,2n^2+3n\right)}
 și mulțimea 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 M}
 a punctelor din plan cuprinse între graficele funcțiilor 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 f}
 și 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 g}
 și dreapta 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 AB}
. Aflați numărul punctelor din 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 M}
 care au ambele coordonate întregi.

@@ Line 3: / Line 3: @@
 ''Suma a două  numere naturale, pare, consecutive este <math>90</math>. Aflați produsul acestor numere.''
+'''[[28868]] (Andre Horvat-Marc)'''
+''Fie <math>n\in \mathbb{N^\ast}</math> și funcțiile <math>f:\left[0,2n^2+3n\right] \to \left[1,2n+1\right]</math>,  <math> f\left(x\right) = \frac{\sqrt{8x+9}-1}{2}</math>
+ și <math> g:\left[1,2n+1\right] \to \left[0,2n^2+3n\right]</math>, <math> g\left(x\right) = f^{-1}\left(x\right)</math>.Fie punctele <math>A\left(2n^2+3n,2n+1\right)</math>, <math>B\left(2n+1,2n^2+3n\right)</math> și mulțimea <math>M</math> a punctelor din plan cuprinse între graficele funcțiilor <math>f</math> și <math>g</math> și dreapta <math>AB</math>. Aflați numărul punctelor din <math>M</math> care au ambele coordonate întregi.''