Find positive integers (a,b) so that:
\((37+20\sqrt{3})^2=a+b\sqrt{3}\)
Expanding the L.H.S:
\(1369+1480\sqrt{3}+1200=a+b\sqrt{3}\)
\(2569+1480\sqrt{3}=a+b\sqrt{3}\)
So it must follow that, by comparing coefficients:
\(a=1369+1200=2569\)
\(b=1480\)
Hope this helps!
