Xác định số hạng đầu và công sai của mỗi cấp số cộng sau đây biết

a) \begin{cases}u_{1}+2u_{5}=0 \\ u_{1}+u_{2}+...+u_{14}=14 \end{cases}{u1+2u5=0u1+u2+...+u14=14
a) \begin{cases}u_{1}+2u_{5}=0 \\ u_{1}+u_{2}+...+u_{14}=14 \end{cases}

b)
\begin{cases}u_{1}+u_{2}+u_{3}=27 \\ u_{1}^{2}+u_{2}^{2}+u_{3}^{2}=275 \end{cases}

bị xóa vì bị trùng bởi rainy.pupi_alwaysfeellonely@yahoo.com.vn, Đức Vỹ 08-01-14 09:04 AM

Câu hỏi này có nội dung hoàn toàn trùng với câu hỏi đã có.

\[\left\{ {\begin{array}{*{20}{l}}
{{u_1} + {u_2} + {u_3} = 27}\\
{u_1^2 + u_2^2 + u_3^2 = 275}
\end{array}} \right.\]
\[ \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
{{u_1} + \frac{{{u_1} + {u_3}}}{2} + {u_3} = 27}\\
{u_1^2 + {{\left( {\frac{{{u_1} + {u_3}}}{2}} \right)}^2} + u_3^2 = 275}
\end{array}} \right.\]
\[ \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
  {{u_1} + {u_3} = 18} \\
  {u_1^2 + u_3^2 = 194}
\end{array}} \right.\]
\[ \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
  {{u_1} + {u_3} = 18} \\
  {{u_1}{u_3} = 65}
\end{array}} \right.\]
$\Rightarrow u_1,u_3$ là nghiệm của pt ${x^2} - 18x + 65 = 0$
\[ \Rightarrow \left\{ \begin{array}{l}
{u_1} = 13\\
{u_3} = 5
\end{array} \right. \vee \left\{ \begin{array}{l}
{u_1} = 5\\
{u_3} = 13
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
{u_1} = 13\\
d =  - 4
\end{array} \right. \vee \left\{ \begin{array}{l}
{u_1} = 5\\
{u_3} = 4
\end{array} \right.\]
\[\left\{ {\begin{array}{*{20}{l}}
  {{u_1} + 2{u_5} = 0} \\
  {{u_1} + {u_2} + ... + {u_{14}} = 14}
\end{array}} \right.\]
\[ \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
  {{u_1} + 2({u_1} + 4d) = 0} \\
  {14{u_1} + \frac{{14(14 - 1)}}{2}d = 14}
\end{array}} \right.\]
\[ \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
  {3{u_1} + 8d = 0} \\
  {14{u_1} + 91d = 14}
\end{array}} \right.\]
\[ \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
  {{u_1} =  - \frac{{16}}{{23}}} \\
  {d = \frac{6}{{23}}}
\end{array}} \right.\]
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