Question

aflati nr de forma xy in baza 10 care sunt cu 45 mai mari decat yx

Answer 1

   
[tex]\displaystyle \\ \overline{xy} - \overline{yx} = 45 \\ \\ 10x+y - (10y+x) = 45 \\ \\ 10x+y - 10y-x = 45 \\ \\ 10x - x +y - 10y = 45 \\ \\ 9x -9y = 45\\\\ 9(x-y)=45\\\\ x-y= \frac{45}{9} \\ \\ \boxed{x-y = 5}\\\\ \text{Solutii: }\\\\ x=9~si~y = 4\\ x=8~si~y = 3\\ x=7~si~y = 2\\ x=6~si~y = 1\\\\ \Longrightarrow~~\overline{xy} \in \{94;~83;~72;~61\}\\\\ \text{Verificare: } \\ 94 - 49 = 45 \\ 83-38 = 45\\ 72-27=45\\ 61-16 = 45 [/tex]