Question

cmr: a=\(n^3\left(n^2-7\right)^2-36n⋮7\) với mọi n

Answer 1

\(=n\left(n^3-7n-36\right)\)

\(=n\left(n^3-4n^2+4n^2-16n+9n-36\right)\)

\(=n\left(n-4\right)\left(n^2+4n+9\right)\)

TH1: n=7k

\(A=7k\left(7k-4\right)\cdot B⋮7\)

TH2: n=7k+1

\(A=\left(7k+1\right)\left(7k-3\right)\left(49k^2-14k+1+28k+4+9\right)\)

\(=\left(7k+1\right)\left(7k-3\right)\left(49k^2+14k+14\right)⋮7\)

TH3: n=7k+2

\(A=\left(7k+2\right)\left(7k-2\right)\left(49k^2+28k+4+28k+8+9\right)\)

\(=C\cdot\left(49k^2+56k+14\right)⋮7\)

Nếu n=10 thì A ko chia hết cho 7 nha bạn