Question

Determinați numerele naturale xy știind ca x3y + y7x = 504

Answer 1

$\overbar{x3y}+\overbar{y7x}=504\\</p><p>\\ 100x+30+y+100y+70+x=504\\</p><p>\\ 101x+101y+100=504~|-100\\</p><p>\\ 101(x+y)=404~|:101\\</p><p>\\ x+y=4\\</p><p>\\ \\</p><p>\\ \overbar{xy}~e~un~nr~natural~de~doua~cifre \Rightarrow x~nu~poate~fi~0\\</p><p>\\ \\</p><p>\\ Cazul~1:~y=0 \Rightarrow x=4\\</p><p>\\ Cazul~2:~y=1 \Rightarrow x=3\\</p><p>\\ Cazul~3:~y=2 \Rightarrow x=2\\</p><p>\\ Cazul~4:~y=3 \Rightarrow x=1\\</p><p>\\ \\</p><p>\\ \overbar{xy} \in \{40,~31,~22,~13\}$