Question

b) c/m (7n-2)² - (2n-7)² chia hết cho 9. với n thuộc z

Answer 1

Ta có: \(\left(7n-2\right)^2-\left(2n-7\right)^2\)

\(=\left(49n^2-14n+4\right)-\left(4n^2-14n+49\right)\)

\(=49n^2-14n+4-4n^2+14n-49\)

\(=45n^2-45\)

\(=9\left(5n^2-5\right)⋮9\) với \(n\in Z\rightarrowĐPCM.\)

Answer 2

Ta có : (7n-2)²-(2n-7)²

⁼ 7n²-2²-2n²+7²

=7n²-2n²+[ -2²+7²]

=n².(7-2) +45

=n².5 +45

Mà 45 ^\(⋮\) 9

=> n².5 + 45 ^\(⋮\) 9

Vậy (7n-2)²-(2n-7)^{2 \(⋮\)} 9

Answer 3

cần gắp