Question

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Aflati nr ab stiind ca ab+ba=99

Answer 1

ab=10a+b

ba=10b+a

ab+ba=11a+11b=11(a+b)=99

a+b=9

ab∈18,27,36,45,54,63,72,81

Answer 2

ab + ba =99

ab descompus in baza 10 = 10a + b

ba =10b +a

ab+ ba = 10a +b +10b +a =11 (a+b)

11(a+b)=99 simplificam cu 11

a + b =9

a si b pot avea valori de la 1 la 8

1+8; 2+7, 3+6, 4+5 si 5+4, 6+3 si 7+2

atunci produsul ab poate fi ( 1×8=8; 2×7=14; 3×6=18 si 4×5=20)

deci ab∈{ 8,14,18,20}