Determinati numarul natural abc daca abc+ab+c=444

Răspuns :

abc+

bc

c

444

3×c=24

c=24÷3=8

+2

ab8+

b8

8

444

b× 2+2= 14

b×2=14-2=12

b=12÷2=6

+1

a68+

68

8

444

a×1+1=4

a×1=a=4-1=3

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abc+ab+c=444

10•ab+c+ab+c=444

11•ab+2c=444

11•ab=444-2c; => ab=numar par

2c≤18; (pentru c maxim 9)

=> 11•ab≥444-18

11•ab≥426 si ab par

=> ab=40;    (11·38=418)

11•40=444-2c

440=444-2c=> c=2

402+40+2=444