Question

CMR:

a, 75⁶ - 45⁶ ⋮ 3600

b, x³ + 3x - bx - ( a³ - b³ ) = 0

c, 7¹⁹ + 7²⁰ + 7²¹ ⋮ 57

Answer 1

a) \(75^6-45^6\)

\(=\left(75^2\right)^3-\left(45^2\right)^3\)

\(=\left(75^2-45^2\right)\left(75^4+75^2.45^2+45^4\right)\)

\(=\left(75-45\right)\left(75+45\right)\left(75^4+75^2.45^2+45^4\right)\)

\(=30.120.\left(75^4+75^2.45^2+45^4\right)\)

\(=3600\left(75^4+75^2.45^2+45^4\right)⋮3600\)

b) Xem lại đề

c) \(7^{19}+7^{20}+7^{21}\)

\(=7^{19}\left(1+7+7^2\right)\)

\(=7^{19}.57⋮57\)