Question

aflati cifrele a si b din relatia a,(b)+0,(3)=1,(3)

Answer 1

e foarte usor.
a=1
b=3
1,(3)+0,(3)=1,(3)

Answer 2

[tex]\overline{a,(b)}+0,(3)=1,(3)\\ a\dfrac{b}{9}+\dfrac{1}{3}=1\dfrac{3}{9}\\ \dfrac{9a+b}{9}+\dfrac{1}{3}=\dfrac{12}{9} [/tex]
[tex]\dfrac{9a+b}{9}=\dfrac{4}{3}-\dfrac{1}{3}\\ \dfrac{9a+b}{9}=1\\ 9a+b=9\\ b=9(1-a)\\ Dar\ cum\ b\leq 9\Rightarrow 9(1-a)\leq 9\\ ~~~~~~~~~~~~~~~~~~~~~~~~ 1-a\leq 1\\ Tinand\ cont\ ca: a\in \mathbb{N}\Rightarrow a\in \{0,1\}\\ Daca\ a=0\Rightarrow b=9\\ Daca\ a=1\Rightarrow b=0\\ S:(a,b)\in \{(0,9); (1,0)\}[/tex]