Question

[Ekachido Rika]

Chứng tỏ rằng: \(4^{2010}+2^{2014}\)\(⋮10\)

Answer 1

[Xyz OLM]

Ta có : 4²⁰¹⁰ = 4^2.1005 = (4²)¹⁰⁰⁵ = (...6)¹⁰⁰⁵ = ...6

Lại có 2²⁰¹⁴ = 2²⁰¹².2² = 2^4.503 . 4 = (2⁴)⁵⁰³ . 4 = (...6)⁵⁰³ . 4 = (...6) . 4 = ...4

Khi đó 4²⁰¹⁰ + 2²⁰¹⁴ = (...6) + (...4) = (...0) \(⋮\)10 (đpcm)

Answer 2

[Fudo]

                                                      Bài giải

                      Ta có : 

\(4^{2010}+2^{2014}=\left(4^2\right)^{1005}+\left(2^4\right)^{503}\cdot2^2=\overline{\left(...6\right)}^{1005}+\overline{\left(...6\right)}^{503}\cdot4=\overline{\left(...6\right)}+\overline{\left(...6\right)}\cdot4\)

\(=\overline{\left(...6\right)}+\overline{\left(...4\right)}=\overline{\left(...0\right)}\text{ }⋮\text{ }10\)

Vậy \(4^{2010}+2^{2014}\text{ }⋮\text{ }10\text{ }\left(ĐPCM\right)\)