Xin chào,xin chào^^
Ta có:$a.b$=$420.21$=$8820$
Mặt $\neq$ : $a+21=b⇔a=b-21$
Ta lại có:$a.b=(b-21).b=8820$
$⇔$ $b.b - 21b = 8820$
$⇔$ $b^{2}$ - $21b = 8820$
$⇔$ $b^{2}$ + $84b$ - $105b$ =$8820$
$⇔$ $b^{2}$ + $84b$ - $105b$ -$8820$=$0$
$⇔$ $b$.($b+84$) - $105$.($b+84$) = $0$
$⇔$ ($b-105$)($b+84$)=$0$
$⇒$ \(\left[ \begin{array}{l}b-105=0\\b+84=0\end{array} \right.\)
$⇒$ \(\left[ \begin{array}{l}b=105\\b=-84\end{array} \right.\)
Mà $b$ là số tự nhiên.$⇒$ $b=105$$⇔$$a=105-21=84$
Vậy ($a;b$)=($84;105$)