Question

Determinati x si y in baza 10, astfel incat:

Answer 1

x,y(barat)+ y,x(barat)=6.6
x+y*$10^{-1}$ + y+ x* $10^{-1}$ = 6.6
$\frac{11}{10} x+\frac{11}{10} y = 6.6$
$\frac{11}{10}(x+y)=6.6$
x+y=6.6* $\frac{10}{11}$
x+y=6
=>(x,y)∈{(1;3);(2;2);(3;1)}

Observatie: $a^{-n}= \frac{1}{ a^{n} }$

Answer 2

[tex]\it \overline{x,y} + \overline{y,x} =6,6|_{\cdot10} \Rightarrow \overline{xy}+ \overline{yx}=66 \Rightarrow 10x+y+10y+x=66 \Rightarrow \\\;\\ \Rightarrow 11x+11y=66 \Rightarrow 11(x+y)=66|_{:11} \Rightarrow x+y=6 \ \ \ \ (1)[/tex]

[tex]\it 6 = 1+5=2+4=3+3=4+2=5+1 \ \ \ \ (2) \\\;\\ (1),\ \ (2) \Rightarrow (x,\ y) \in \{ (1,\ 5),\ (2,\ 4),\ (3,\ 3),\ (4,\ 2),\ (5,\ 1)\} [/tex]