Question

[Linh nguyen thuy]

Chứng tỏ rằng:

\(\overline{ab}\) - \(\overline{ba}\) \(⋮\) 9 ( a > b )

\(\overline{abba}\) \(⋮\) 11

Answer 1

[Trần Lê Lâm Nguyên]

ab - ba ⋮ 9

ab - ba=a * 10+b*1-b*10-a*1

=a*(10-1)-b*(10-1)=a*9-b*9=9*(a-b)⋮9(vì 9⋮9)

vậy ab-ba⋮9

abba ⋮ 11

abba=a*1000+b*100+b*10+a.1=a*(1000+1)+b*(100+10)

=a*1001+b*110=a*11*91+b*10*11=11(a*91+b*10)⋮11(vì 11⋮11)

Vậy abba⋮11

Answer 2

[Trần Ngọc Phú]

ab - ba ⋮ 9

ab - ba=a x 10+b x 1-b x 10-a x 1

=a x (10-1)-b x (10-1)=a x 9-b x 9=9x (a-b)⋮9(vì 9⋮9)vậy ab-ba⋮9abba ⋮11

abba=a x 1000+b x 100+b x 10+a.1= a x (1000+1)+b x (100+10)

=a x 1001+b x 110=a x 11 x 91+b x 10 x 11=11(a x 91+b x 10)⋮11(vì 11⋮11)Vậy abba⋮11