Question

chứng minh rằng 8^12-2^33-2^30chia hết cho 55

Answer 1

Ta có: 

8¹² - 2³³ - 2³⁰

= (2³)¹² - 2³³ - 2³⁰

= 2³⁶ - 2³³ - 2³⁰

= 2³⁰.(2⁶ - 2³ - 1)

= 2³⁰.(64 - 8 - 1)

= 2³⁰.55 chia hết cho 55 (đpcm)

Answer 2

Ta có:

\(8^{12}-2^{33}-2^{30}\)

\(=8^{12}-\left(2^3\right)^{11}-\left(2^3\right)^{10}\)

\(=8^{12}-8^{11}-8^{10}\)

\(=8^{10}\left(8^2-8-1\right)\)

\(=8^{10}.55⋮55\)

\(\Rightarrow8^{12}-2^{33}-2^{30}⋮55\left(đpcm\right)\)