[tex]a\cdot b=375\\
(a+5)(b-5)=500\\
a\cdot b+5b-5a-25=500\\
375+5b-5a=525\\
5b-5a=150\\
b-a=30\Rightarrow b=30+a\\
Inlocuim\ in\ prima\ relatie:\\
a\cdot (30+a)=375\\
a^2+30a-375=0\\
\Delta=900+4\cdot 375 =2400\Rightarrow \sqrt{\Delta}=20\sqrt6\\
a_1=\frac{-30+20\sqrt6}{2}=10\sqrt6-15\\
a_2=\frac{-30-20\sqrt6}{2}=-15-10\sqrt6\\
Pt.\ a=10\sqrt6 -15:\\
b=\frac{375}{10\sqrt6-15}=\frac{375(10\sqrt6+15)}{375}=10\sqrt6+15\\
\\
Pt.\ a=-10\sqrt6-15:\\
[/tex]
[tex]b=-\frac{375}{10\sqrt6-15}=-\frac{375(10\sqrt6+15)}{375}= -10\sqrt6-15\\
Asadar:\\
S:(a,b)\in \{(10\sqrt6-15;10\sqrt6+15), (-10\sqrt6-15; -10\sqrt6-15)\}[/tex]