\[\begin{array}{l}
2)\,\,{3^x} + {4^x} = {5^x}\,\,\,\left( * \right)\\
Xet\,\,ham\,\,so:\,\,f\left( x \right) = {3^x} + {4^x}\\
\Rightarrow f'\left( x \right) = {3^x}\ln 3 + {4^x}\ln 4 > 0\\
\Rightarrow hs\,\,\,y = f\left( x \right)\,\,\,DB\,\,tren\,\,R.\\
Xet\,\,ham\,\,so:\,\,g\left( x \right) = {5^x}\\
\Rightarrow g'\left( x \right) = {5^x}\ln 5 > 0\\
\Rightarrow hs\,\,DB\,\,tren\,\,\,R.\\
\Rightarrow \left( * \right)\,\,\,co\,\,nghiem\,\,thi\,\,co\,\,nghiem\,\,duy\,\,nhat.\\
Ta\,\,thay\,\,f\left( 2 \right) = g\left( 2 \right) = 25\\
\Rightarrow x = 2\,\,\,la\,\,\,nghiem\,\,cua\,\,\,pt.
\end{array}\]
Câu 1 em xem lại đã đúng đề bài chưa nhé!
