Question

a/ Tính nhanh: 2000²-1995(2000+5)

b/ CMR: a⁵-a ⋮ 5 với mọi a ∈ Z

Answer 1

\(a^5-a=a\left(a^4-1\right)=a\left(a^2+1\right)\left(a^2-1\right)\)

\(=a\left(a-1\right)\left(a+1\right)\left(a^2+1\right)\)

\(=a\left(a-1\right)\left(a+1\right)\left(a^2-4+5\right)=a\left(a-1\right)\left(a+1\right)\left(a^2-4\right)+5a\left(a-1\right)\left(a+1\right)\)

\(=a\left(a-1\right)\left(a+1\right)\left(a-2\right)\left(a+2\right)+5a\left(a-1\right)\left(a+1\right)⋮5\)

Answer 2

a) \(2000^2-1995\left(2000+5\right)\)

\(=2000^2-2000\left(2000+5\right)+5\left(2000+5\right)\)

\(=2000^2-2000^2-10000+10000+25\)

\(=25\)

b) bó tay