Đáp án:

Giải thích các bước giải:

$A = (2008^{2007} + 2007^{2007})^{2008}$

$= \left[ 2008^{2007} \cdot \left( 1 + \left( \dfrac{2007}{2008} \right)^{2007} \right) \right]^{2008}$

$= 2008^{2007 \cdot 2008} \cdot \left( 1 + \left( \dfrac{2007}{2008} \right)^{2007} \right)^{2008}$

$B = (2008^{2008} + 2007^{2008})^{2007}$

$= \left[ 2008^{2008} \cdot \left( 1 + \left( \dfrac{2007}{2008} \right)^{2008} \right) \right]^{2007}$

$= 2008^{2008 \cdot 2007} \cdot \left( 1 + \left( \dfrac{2007}{2008} \right)^{2008} \right)^{2007}$

$r = \dfrac{2007}{2008}$ ($0 < r < 1$)

$r^{2007} > r^{2008} \Rightarrow 1 + r^{2007} > 1 + r^{2008} > 1$

$\left( 1 + r^{2007} \right)^{2008} > \left( 1 + r^{2007} \right)^{2007}$

Mà $1 + r^{2007} > 1 + r^{2008}$

$\Rightarrow \left( 1 + r^{2007} \right)^{2007} > \left( 1 + r^{2008} \right)^{2007}$

$\Rightarrow \left( 1 + r^{2007} \right)^{2008} > \left( 1 + r^{2008} \right)^{2007}$

$\Rightarrow A > B$