Question

2,1(a)+2,a(1)=a,1(2)+1,a(2) in baza 10 determinati cifra a

Answer 1

[tex]\overline{2,1(a)}+\overline{2,a(1)}=\overline{a,1(2)}+\overline{1,a(2)}\\ 2\frac{\overline{1a}-1}{90}+2\frac{\overline{a1}-a}{90}=a\frac{12-1}{90}+1\frac{\overline{a2}-a}{90}\\ \\ \frac{180+10+a-1}{90}+\frac{180+10a+1-a}{90}=\frac{90a+11}{90}+\frac{90+10a+2-a}{90} |\cdot 90\\ 189+a+181+9a=90a+11+92+9a\\ 370+10a=99a+103\\ 267=89a\Rightarrow\boxed{a=3}\\[/tex]