Đáp án:
\(\left[ \begin{array}{l}
A = 86 + \dfrac{{43 + 5\sqrt {61} }}{2}\\
A = 86 + \dfrac{{43 - 5\sqrt {61} }}{2}
\end{array} \right.\)
Giải thích các bước giải:
Xét:
Δ=\(25 - 4.\left( { - 9} \right) = 61\)
\(\begin{array}{l}
\to \left[ \begin{array}{l}
x = \dfrac{{5 + \sqrt {61} }}{2}\\
x = \dfrac{{5 - \sqrt {61} }}{2}
\end{array} \right.\\
Có:A = 2\left( {{x_1}^2 + {x_2}^2} \right) + {x_2}^2\\
= 2\left[ {{{\left( {{x_1} + {x_2}} \right)}^2} - 2{x_1}{x_2}} \right] + {x_2}^2\\
\to \left[ \begin{array}{l}
A = 2\left( {25 - 2.\left( { - 9} \right)} \right) + {\left( {\dfrac{{5 + \sqrt {61} }}{2}} \right)^2}\\
A = 2\left( {25 - 2.\left( { - 9} \right)} \right) + {\left( {\dfrac{{5 - \sqrt {61} }}{2}} \right)^2}
\end{array} \right.\\
\to \left[ \begin{array}{l}
A = 86 + \dfrac{{43 + 5\sqrt {61} }}{2}\\
A = 86 + \dfrac{{43 - 5\sqrt {61} }}{2}
\end{array} \right.
\end{array}\)
