Question

determinati toate numerele de forma XY care sunt cu 45 mari decat YX

Answer 1

   
[tex]\displaystyle\\ \overline{xy} - \overline{yx}=45\\ 10x+y - (10y+x) = 45\\ 10x+y - 10y-x = 45\\ 9x - 9y = 45\\ 9(x-y) = 45\\\\ x-y = \frac{45}{9} \\\\ x-y = 5\\\\ Solutii:\\ S_1:~~~x=6; ~~~y = 1\\ S_2:~~~x=7; ~~~y = 2\\ S_3:~~~x=8; ~~~y = 3\\ S_4:~~~x=9; ~~~y = 4\\\\ \Longrightarrow~~\boxed{\bf \overline{xy}~ \in ~\{61;~72;~83;~94\}} [/tex]