Question

Answer 1

a: \(n^3+17n=n^3-n+18n=n\left(n-1\right)\left(n+1\right)+18n\)

Vì n;n-1;n+1 là ba số nguyênliên tiếp

nên \(n\left(n-1\right)\left(n+1\right)⋮3!=6\)

mà \(18n⋮6\)

nên \(n\left(n-1\right)\left(n+1\right)+18n⋮6\)

=>\(n^3+17n⋮6\)

b: \(\dfrac{\left(x^2+a\right)\left(1+a\right)+a^2x^2+1}{\left(x^2-a\right)\left(1-a\right)+a^2x^2+1}\)

\(=\dfrac{x^2+x^2a+a+a^2+a^2x^2+1}{x^2-x^2a-a+a^2+a^2x^2+1}\)

\(=\dfrac{x^2\left(a^2+a+1\right)+\left(a^2+a+1\right)}{x^2\left(a^2-a+1\right)+\left(a^2-a+1\right)}\)

\(=\dfrac{\left(a^2+a+1\right)\left(x^2+1\right)}{\left(a^2-a+1\right)\left(x^2+1\right)}=\dfrac{a^2+a+1}{a^2-a+1}\)