Question

Chứng minh:

\(x^{50}+x^{10}+8⋮x^{20}+x^{10}+1\)

Answer 1

ko bt bn giải ra chưa nx nhưng mk giả thử nhé!

bn sửa lại đề: \(x^{50}+x^{20}+1⋮x^{20}+x^{10}+1\)

\(x^{50}+x^{20}+1=x^{50}-x^{20}+x^{20}+x^{10}+1\)\(=x^{20}\left(x^{30}-1\right)+x^{20}+x^{10}+1\)

\(=x^{20}[\left(x^{10}\right)^3-1]+x^{20}+x^{10}+1\)

\(=x^{20}\left(x^{10}-1\right)\left(x^{20}+x^{10}+1\right)+x^{20}+x^{10}+1\)\(=\left(x^{20}+x^{10}+1\right)[x^{20}\left(x^{10}-1\right)+1]\)

Từ đó suy ra đpcm