Chứng minh rằng: A=742^3 – 692^3 : 200 B= 685^3 + 315^3 : 25000

Giải thích các bước giải:

 $a) 742^3-692^3\\
=(742-692).(742^2+742.692+692^2)\\
=50.(742^2+742.692+692^2)$
Do $742\vdots 2\Rightarrow 742^2\vdots 4$
${\left[\begin{aligned}742\vdots 2\\692\vdots 2\end{aligned}\right.}\Rightarrow 742.692\vdots 4\\
692\vdots 2\Rightarrow 692^2\vdots 4\\
\Rightarrow (742^2+742.692+692^2)\vdots 4\\
\Rightarrow (742^3-692^3)\vdots (50.4)\Rightarrow (742^3-692^3)\vdots 200$

$B= 685^3 + 315^3 \\
=(685+315)(685^2+685.315+315^2)\\
=1000.(685^2+685.315+315^2)$
Ta có$ 685\vdots 5\Rightarrow 685^2\vdots 25$
${\left[\begin{aligned}685\vdots 5\\315\vdots 5\end{aligned}\right.}\Rightarrow 685.315\vdots 25\\
315\vdots 5\Rightarrow 315^2\vdots 25\\
\Rightarrow (685^2+685.315+315^2)\vdots 25\\
\Rightarrow (685^3-315^3)\vdots (25.1000)\Rightarrow (685^3-315^3)\vdots 25000$