E:5743: Difference between revisions
No edit summary |
No edit summary |
||
| Line 5: | Line 5: | ||
Soliție | Soliție | ||
Dacă <math>15 | \overline{7a8b}</math>, atunci <math>5 | \overline{7a8b}</math> și <math>3 | \overline{7a8b}</math><math>. Din <math>5 | \overline{7a8b}</math>, se obține <math> b \in \left\{0,5\right\}. Din <math>3 | \overline{7a8b}</math>, se obține <math> a+b \in \mathcal{M}_3</mathh>. | Dacă <math>15 | \overline{7a8b}</math>, atunci <math>5 | \overline{7a8b}</math> și <math>3 | \overline{7a8b}</math><math>. Din <math>5 | \overline{7a8b}</math>, se obține <math> b \in \left\{0,5\right\}</mathh>. Din <math>3 | \overline{7a8b}</math>, se obține <math> a+b \in \mathcal{M}_3</mathh>. Pentru <math>b=0</math> rezultă <math> a \in \left\{0,3,6,9\right\}. Pentru <math>b=5</math> rezultă <math> a \in \left\{1,4,7\right\}. Deci | ||
Revision as of 04:38, 8 December 2024
E:5743 (Grigore Balog)
Fie mulțimea numerelor de forma , care se divid cu 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 B} mulțimea numerelor de forma 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 \overline{7x8y}} , care se divid cu 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 40} . Să se determine mulțimile 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 \cup B} , 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\cap B} 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 A\setminus B} .
Soliție
Dacă 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 15 | \overline{7a8b}} , atunci 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 5 | \overline{7a8b}} 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 3 | \overline{7a8b}} 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 . Din <math>5 | \overline{7a8b}} , se obține 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 \in \left\{0,5\right\}</mathh>. Din <math>3 | \overline{7a8b}} , se obține 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 \mathcal{M}_3</mathh>. Pentru <math>b=0} rezultă 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 \in \left\{0,3,6,9\right\}. Pentru <math>b=5} rezultă <math> a \in \left\{1,4,7\right\}. Deci