Question

Determina numarul natural ab scris in baza 10 stiind ca diferenta dintre el si rasturnatul sau este 18.Cate solutii se obtin?Enumerati solutiile.exercitiul 14 poza

Answer 1

ab = numarul

ba = rasturnatul sau

ab - ba = 18

10 × a + b - 10 × b - a = 18

9 × a - 9 × b = 18

9 × ( a - b) = 18

a - b = 18 : 9 = 2

9 - 7 = 2
8 - 6 = 2
7 - 5 = 2
6 - 4 = 2
5 - 3 = 2
4 - 2 = 2
3 - 1 = 2

ab = 97; 86; 75;64; 53; 42;31 .
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Answer 2

$\it \overline{ab}-\overline{ba}=18\Rightarrow 10a+b-(10b+a)=18\Rightarrow10a+b-10b-a=18 \Rightarrow\\\\\Rightarrow9a-9b=18|_{:9}\Rightarrow a-b=2\Rightarrow \overline{ab}\in\{97,86,75,64,53,42,31\}$