Question

determinati cifrele a si b astfel incat 9/a+b =0,b+a,2cu bara-0,2

Answer 1

9/a+b=0,b+a,2-0,2 ⇔
9/a+b=b/9+a2/10-2/10 ⇔
9/a+b=b/9+(a2-2)/10 ⇔
9/a+b=b/9+10a/10 ⇔
9/a+b=b/9+a ⇔
(a+b)(b/9+a)=9 ⇔
(a+b)(b+9a)/9=9 ⇒(a+b)(b+9a)=81
Avem urmatoarele variante
81=1·81⇒a+b=1 si b+9a=81
a+b=1 si b+9a=81 ⇒8a=80⇒a=10⇒fals deoarece 10 nu este cifra;
81=3·27⇒a+b=3 si b+9a=27
a+b=3 si b+9a=27 ⇒8a=24⇒a=3⇒b=0⇒convine;
81=9·9⇒a+b=9 si b+9a=9
a+b=9 si b+9a=9 ⇒8a=0⇒a=0⇒b=9⇒convine;
81=27·3⇒a+b=27 si b+9a=3⇒nu convine varianta deoarece a;b=cifre asadar a+b≤9+9=18 unde 18≠27;
81=81·1⇒a+b=81 si b+9a=1⇒nu convine varianta deoarece a;b=cifre asadar a+b≤9+9=18 unde 18≠81.
In concluzie avem
(a;b)∈{(3;0),(0;9)}