Cho một cấp số nhân ( u n ) có công bội q thỏa mãn { u5 + u2 = 36; u6 − u4 = 48 . Tính u1 + 2024q .

\(\left\{ \begin{array}{l}{u_5} + {u_2} = 36\\{u_6} - {u_4} = 48\end{array} \right.\)\( \Leftrightarrow \left\{ \begin{array}{l}{u_1}{q^4} + {u_1}q = 36\\{u_1}{q^5} - {u_1}{q^3} = 48\end{array} \right.\)\[ \Leftrightarrow \left\{ \begin{array}{l}{u_1}q\left( {{q^3} + 1} \right) = 36\\{u_1}{q^3}\left( {{q^2} - 1} \right) = 48\end{array} \right.\]\[ \Leftrightarrow \left\{ \begin{array}{l}{u_1}q\left( {q + 1} \right)\left( {{q^2} - q + 1} \right) = 36\\{u_1}{q^3}\left( {q - 1} \right)\left( {q + 1} \right) = 48\end{array} \right.\]

⇔u1qq+1q2−q+1=3636q2q−1q2−q+1=48 ⇔u1qq+1q2−q+1=363q2q−1=4q2−q+1 ⇔u1qq+1q2−q+1=363q3−7q2+4q−4=0 ⇔u1⋅22+122−2+1=36q=2 ⇔u1=2q=2

Vậy \({u_1} + 2024q = 2 + 2024 \cdot 2 = 4050\).

Trả lời: 4050.