S:P18.12: Difference between revisions

Revision as of 12:12, 16 December 2024

S:P18.12 (Vasile Berinde)

Reconstituiți înmulțirea 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{abc} \times 3 = \overline{bcc}} .

Soluție.

Notăm prin 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 u\left( N \right)} ultima cifră a numărului natural 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} .

Avem 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{abc} \times 3 = \overline{bcc} \Rightarrow 300a+30b+3c=100b+11c \Rightarrow 300a = 70b + 8c} .

Cum $u\left(300a\right)=0$ și $u\left(70b\right)=0$ , se deduce că $u\left(8c\right)=0$ , deci avem posibilitățile $c=0$ 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 c=5} .

Pentru 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 c=0} 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=0} , care nu convine.

Pentru 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 c=5} , avem

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 Notăm prin <math>u\left( N \right)</math> ultima cifră a numărului natural <math>N</math>.
-Avem ''<math>\overline{abc} \times 3 = \overline{bcc} \Rightarrow 300a+30b+3c=100b+11c \Rightarrow 300a = 70b + 8c</math>''
+Avem <math>\overline{abc} \times 3 = \overline{bcc} \Rightarrow 300a+30b+3c=100b+11c \Rightarrow 300a = 70b + 8c</math>.
+Cum <math>u\left( 300 a\right) = 0</math> și <math>u\left( 70b \right) = 0</math>, se deduce că <math>u\left( 8c \right) = 0</math>, deci avem posibilitățile <math>c=0</math> și <math>c=5</math>.
+Pentru <math>c=0</math> se obține <math>b=0</math>, care nu convine.
+Pentru <math>c=5</math>, avem