|
|
2.
Phương trình tương đương với:
$\left(\frac{5-\sqrt{21}}{2}\right)^x+7\left(\frac{5+\sqrt{21}}{2}\right)^x=8$
Đặt: $a=\left(\frac{5-\sqrt{21}}{2}\right)^x,b=\left(\frac{5+\sqrt{21}}{2}\right)^x;a,b>0$
Ta có hệ sau:
$\left\{ \begin{array}{l} ab=1\\a+7b=8 \end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l} b=\frac{1}{a}\\a+\frac{7}{a}=8 \end{array} \right.$
$\Leftrightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} a=1\\b=1 \end{array} \right.\\\left\{ \begin{array}{l} a=7\\ b=\frac{1}{7} \end{array} \right. \end{array} \right.$
Suy ra:
$\left[ \begin{array}{l}\left(\frac{5-\sqrt{21}}{2}\right)^x=1 \\\left(\frac{5-\sqrt{21}}{2}\right)^x=7\end{array} \right.\Leftrightarrow \left[\begin{array}{l} x=0\\x=\frac{\ln7}{\ln(5-\sqrt{21})-\ln2} \end{array} \right.$
|