(left{ begin{array}{l}{u_7} - {u_3} = 8\{u_2}{u_7} = 75end{array} right.)
Giải chi tiết:
(left{ begin{array}{l}{u_7} - {u_3} = 8\{u_2}{u_7} = 75end{array} right. Leftrightarrow left{ begin{array}{l}{u_1} + 6d - {u_1} - 2d = 8\left( {{u_1} + d} right)left( {{u_1} + 6d} right) = 75end{array} right.)
(begin{array}{l} Leftrightarrow left{ begin{array}{l}4d = 8\left( {{u_1} + d} right)left( {{u_1} + 6d} right) = 75end{array} right. Leftrightarrow left{ begin{array}{l}d = 2\left( {{u_1} + 2} right)left( {{u_1} + 12} right) = 75end{array} right.\ Leftrightarrow left{ begin{array}{l}d = 2\u_1^2 + 14{u_1} - 51 = 0end{array} right. Leftrightarrow left{ begin{array}{l}d = 2\left[ begin{array}{l}{u_1} = 3\{u_1} = - 17end{array} right.end{array} right.end{array})