Question

Determinati numarul natural xyz scris in baza 10,unde xyz=xy+ yz+zx,x nu este 0

Answer 1

x,y,z - cifre

xyz in baza 10 = 100x +10y+z

dar xyz=xy+yz+zx

=> 100x+10y+z=xy+yz+zx

=>100x+10y+z=10x+y+10y+z+10z+x

=>100x+10y+z=10(x+y+z)+x+y+z

=>100x+10y+z=(x+y+z)(10+1)

=>100x+10y+z=11x+11y+11z

=>89x=y+10z

y+10z scris in baza 10 este: zy

=>89x=zy

=>x nu poate fi 0, si nici mai mare decat 1 => x=1

=>89=zy

=>z=8;y=9

=>nr este:198