Question

chứng minh: 5²⁰¹⁴-5²⁰¹³+5²⁰¹²⋮105

Answer 1

Ta có:

A= 5²⁰¹⁴-5²⁰¹³+5²⁰¹²⋮105

A= 5^2011(5^3- 5^2)+5

A=5^2011(125- 25)+5

A= 5^2011. 105

=> A:105​(đpcm)

Answer 2

5^2014-5^2013+5^2012

=5^2012(5^2-5^1+1)

 =5^2012.21 =5^2011.5.21

=5^2011.105

Vậy 5^2014-5^2013+5^2012 chia hết cho 105

chúc bạn học tốt

Answer 3

Ta có: \(5^{2014}-5^{2013}+5^{2012}\)

\(=5^{2012}\cdot\left(5^2-5+1\right)\)

\(=5^{2011}\cdot5\cdot21\)

\(=5^{2011}\cdot105⋮105\)(đpcm)