\[\begin{array}{l} \sqrt[x]{{x + 56}} = 6\\ \Leftrightarrow x + 56 = {6^x}\,\,\,\left( * \right)\\ Xet\,\,ham\,\,\,so:\,\,\,\,f\left( x \right) = x + 56\\ \Rightarrow f’\left( x \right) = 1 > 0\\ \Rightarrow hs\,\,\,\,DB\,\,tren\,\,\,R.\\ Xet\,\,ham\,\,so\,\,\,g\left( x \right) = {6^x}\\ \Rightarrow g’\left( x \right) = {6^x}\ln 6 > 0\\ \Rightarrow hs\,\,\,DB\,\,tren\,\,R.\\ \Rightarrow \left( * \right)\,\,\,co\,\,\,nghiem\,\,\,thi\,\,\,co\,\,\,nghiem\,\,\,duy\,\,nhat.\\ Ma\,\,\,\,\left\{ \begin{array}{l} g\left( 3 \right) = \,{6^3} = 216\\ f\left( 3 \right) = 59 \end{array} \right.\\ Khi\,\,\,x\,\,cang\,\,\tan g\,\,ta\,\,\,thay\,\,\,g\left( x \right)\,\,\tan g\,\,nhanh\,\,\,hon\,\,\,f\left( x \right)\\ \Rightarrow \left( * \right)\,\,\,vo\,\,\,nghiem. \end{array}\] Bình luận
\[\begin{array}{l}
\sqrt[x]{{x + 56}} = 6\\
\Leftrightarrow x + 56 = {6^x}\,\,\,\left( * \right)\\
Xet\,\,ham\,\,\,so:\,\,\,\,f\left( x \right) = x + 56\\
\Rightarrow f’\left( x \right) = 1 > 0\\
\Rightarrow hs\,\,\,\,DB\,\,tren\,\,\,R.\\
Xet\,\,ham\,\,so\,\,\,g\left( x \right) = {6^x}\\
\Rightarrow g’\left( x \right) = {6^x}\ln 6 > 0\\
\Rightarrow hs\,\,\,DB\,\,tren\,\,R.\\
\Rightarrow \left( * \right)\,\,\,co\,\,\,nghiem\,\,\,thi\,\,\,co\,\,\,nghiem\,\,\,duy\,\,nhat.\\
Ma\,\,\,\,\left\{ \begin{array}{l}
g\left( 3 \right) = \,{6^3} = 216\\
f\left( 3 \right) = 59
\end{array} \right.\\
Khi\,\,\,x\,\,cang\,\,\tan g\,\,ta\,\,\,thay\,\,\,g\left( x \right)\,\,\tan g\,\,nhanh\,\,\,hon\,\,\,f\left( x \right)\\
\Rightarrow \left( * \right)\,\,\,vo\,\,\,nghiem.
\end{array}\]