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\(xy=1\)
বা, \(y=\cfrac{1}{x}=\cfrac{\sqrt7-\sqrt3}{\sqrt7+\sqrt3}\)
\(\therefore x+y=\cfrac{\sqrt7+\sqrt3}{\sqrt7-\sqrt3}+\cfrac{\sqrt7-\sqrt3}{\sqrt7+\sqrt3}\)
বা, \(x+y\)

\(=\cfrac{(\sqrt7+\sqrt3)^2+(\sqrt7-\sqrt3)^2}{(\sqrt7+\sqrt3)(\sqrt7-\sqrt3)}\)

\(=\cfrac{2[(\sqrt7)^2+(\sqrt3)^2]}{(\sqrt7)^2-(\sqrt3)^2}\)

\(=\cfrac{2(7+3)}{7-3}\)

\(=\cfrac{20}{4}=5\)

\(\cfrac{x^2+3xy+y^2}{x^2-3xy+y^2}\)
\(= \cfrac{x^2+y^2+3xy}{x^2+y^2-3xy}\)
\(= \cfrac{(x+y)^2-2xy+3xy}{(x+y)^2-2xy-3xy}\)
\(= \cfrac{(x+y)^2+xy}{(x+y)^2-5xy}\)
\(= \cfrac{(5)^2+1}{(5)^2-5\times 1}\)
\(= \cfrac{25+1}{25-5}\)
\(= \cfrac{26}{20}= \cfrac{13}{10}\)