Cấp số nhân : { u1+u2+u3 = 21 and 1/u1 + 1/u2 +1/u3 = 7/12 . tìm u1 và q

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1. Đáp án:

   $\begin{array}{l}
   {u_1} = \frac{{{u_2}}}{q};{u_3} = {u_2}.q\\
   \left\{ \begin{array}{l}
   {u_1} + {u_2} + {u_3} = 21\\
   \frac{1}{{{u_1}}} + \frac{1}{{{u_2}}} + \frac{1}{{{u_3}}} = \frac{7}{{12}}
   \end{array} \right. \Rightarrow \left\{ \begin{array}{l}
   \frac{{{u_2}}}{q} + {u_2} + {u_2}q = 21\\
   \frac{q}{{{u_2}}} + \frac{1}{{{u_2}}} + \frac{1}{{{u_2}q}} = \frac{7}{{12}}
   \end{array} \right.\\
    \Rightarrow \left\{ \begin{array}{l}
   {u_2}\left( {\frac{1}{q} + 1 + q} \right) = 21\\
   \frac{1}{{{u_2}}}\left( {q + 1 + \frac{1}{q}} \right) = \frac{7}{{12}}
   \end{array} \right.\\
    \Rightarrow \left\{ \begin{array}{l}
   u_2^2 = 21:\frac{7}{{12}}\\
   {u_2}\left( {\frac{1}{q} + 1 + q} \right) = 21
   \end{array} \right.\\
    \Rightarrow \left\{ \begin{array}{l}
   {u_2} =  \pm 6\\
   q + \frac{1}{q} + 1 =  \pm \frac{7}{2}
   \end{array} \right.\\
    \Rightarrow \left\{ \begin{array}{l}
   {u_2} =  \pm 6\\
   \left[ \begin{array}{l}
   q = 2\\
   q = \frac{1}{2}\\
   q = \frac{{ – 9 \pm \sqrt {65} }}{4}
   \end{array} \right.
   \end{array} \right.
   \end{array}$

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