Question

care sunt nr de forma xyz stiind ca xy+yz+zx=66 -explicație pt. elev de clasa a IV-a

Answer 1

 

$\displaystyle\\</p><p>\text{Se cer numerele de forma }~\overline{xyz}~\text{ stiind ca } ~ \overline{xy}+\overline{yz}+\overline{zx}=66\\\\</p><p>\text{Rezolvare:}\\\\</p><p>\text{Descompunem in zeci si unitati numerele de 2 cifre.}\\\\</p><p>\overline{xy}+\overline{yz}+\overline{zx}=66\\\\</p><p>10x+y+10y+z+10z+x=66\\\\</p><p>10x+x+10y+y+10z+z=66\\\\</p><p>11x+11y+11z=66\\\\</p><p>11(x+y+z)=66\\\\</p><p>x+y+z = \frac{66}{11}\\\\</p><p>\boxed{\bf x+y+z=6}$

$\Longrightarrow~~\text{Numerele de forma }~\overline{xyz}~\text{ au suma cifrelor egala cu 6.}\\\\</p><p>\Longrightarrow~~\overline{xyz}\in\{114;~123;~132;~141;~213;~222;~ 231;~312;~321;~411\}$