Đáp án:\({u_1} = 1;q=2\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
{u_1} + {u_2} + {u_3} + {u_4} = 15\\
u_1^2 + u_2^2 + u_3^2 + u_4^2 = 85
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
{u_1} + {u_1}.q + {u_1}.{q^2} + {u_1}.{q^3} + {u_1}.{q^4} = 15\\
u_1^2 + u_1^2.{q^2} + u_1^2.{q^4} + u_1^2.{q^6} + u_1^2.{q^5} = 85
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
{u_1}.\frac{{{q^4} - 1}}{{q - 1}} = 15(1)\\
u_1^2.\frac{{{q^8} - 1}}{{{q^2} - 1}} = 85(2)
\end{array} \right.\\
\Rightarrow {u_1}.\frac{{({q^8} - 1)(q - 1)}}{{({q^4} - 1)({q^2} - 1)}} = \frac{{85}}{{15}} \Leftrightarrow {u_1}.\frac{{{q^4} + 1}}{{q + 1}} = \frac{{17}}{3}(3)\\
(1):(3) \Rightarrow \frac{{({q^4} - 1)(q + 1)}}{{({q^4} + 1)(q - 1)}} = \frac{{45}}{{17}} \Rightarrow q = 2\\
\Rightarrow {u_1} = 1\\
\end{array}\)
