Question

1) Arătați că abc-ab-c=9×ab


2)Căte numere de forma abc verifică relația abc-cba=594?

Va rog! Dau coroana!​

Answer 1

1) abc= 100a+10b+c

ab= 10a+b

abc-ab-c=100a+10b+c-10a-b-c= 90a+9b=

=9(10a+b)= 9ab

unde abc si ab au bara deaspura.

2) abc= 100a+10b+c

cba= 100c+10b+a

abc-cba= 100a+10b+c-100c-10b-a= 99a-99c=99(a-c)

99(a-c)= 594

a-c= 6

a=6, c=0 deci nr abc sunt: 610,620,630,640,650,670,680.,690

a=7, c=1 deci nr abc sunt: 701,721,731,741,751,761,781,791

a=8, c=2 deci nr abc sunt: 802, 812,832,...,873,893

a=9, c=3 deci nr abc sunt: 903, 913,923,943,953,963,973,973,983

considerand a#b#c