a*b=420⇒a=420/b
(a+5)(b-2)=400
ab+5b-2a-10=400
420+5b-2*420/b=410
5b-840/b=-10
5b-840/b+10=0
5b²+10b-840=0
[tex]\Delta=100+16800=16900=\ \textgreater \ \sqrt{\Delta}=130\\
b_{1,2}=\frac{-10+-130}{10}\\
b_1=\frac{120}{10}=12\\
b_2=\frac{-140}{10}=-14\\
a)b=12=\ \textgreater \ a*12=420=\ \textgreater \ a=35\\
b)b=-14=\ \textgreater \ a*(-14)=420=\ \textgreater \ a=-30\\
(a,b) apartine \{ (35,12),(-30,-14)\} [/tex]
