Question

Calculati x+y, stiind ca xy+yx este patrat perfect. xy si yx sunt numere nasturale

Answer 1

$\overline{xy} + \overline{yx} = 10x+y+10y+x=11x+11y=11(x+y)-patrat \\ perfect \Rightarrow~x+y=11k^2,~dar~2\ \textless \ x+y \leq 18 \Rightarrow k=1 \Rightarrow \\ \Rightarrow \boxed{x+y=11}.$