Toán Lớp 6: Tìm số nguyên tố n sao cho 4n^2+15 chia hết cho n-2
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 6: Tìm số nguyên tố n sao cho 4n^2+15 chia hết cho n-2
Comments ( 1 )
4{n^2} + 15\\
= 4{n^2} – 16 + 31\\
= 4\left( {{n^2} – 4} \right) + 31\\
= 4.\left( {n + 2} \right).\left( {n – 2} \right) + 31\\
Do:4.\left( {n + 2} \right).\left( {n – 2} \right) \vdots \left( {n – 2} \right)\\
\Leftrightarrow 31 \vdots \left( {n – 2} \right)\\
\Leftrightarrow \left( {n – 2} \right) \in \left\{ { – 31; – 1;1;31} \right\}\\
\Leftrightarrow n \in \left\{ { – 29;1;3;33} \right\}\\
\Leftrightarrow n = 3
\end{array}$