Question

So sánh 7^16 -1 và 8(7^8 +1)(7^4 +1)(7^2 +1)

Answer 1

Ta có: \(8\left(7^8+1\right)\left(7^4+1\right)\left(7^2+1\right)=\frac{1}{6}.48\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\)

\(=\frac{1}{6}\left(7^2-1\right)\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\)

\(=\frac{1}{6}\left(7^4-1\right)\left(7^4+1\right)\left(7^8+1\right)\)

\(=\frac{1}{6}\left(7^8-1\right)\left(7^8+1\right)\)

\(=\frac{1}{6}\left(7^{16}-1\right)\)

Vì  \(7^{16}-1>\frac{1}{6}\left(7^{16}-1\right)\) nên  \(7^{16}-1>8\left(7^8+1\right)\left(7^4+1\right)\left(7^2+1\right)\)