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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, \(x+y\)

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

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

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

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

\(\cfrac{x^2+xy+y^2}{x^2-xy+y^2}\)
\(= \cfrac{x^2+y^2+xy}{x^2+y^2-xy}\)
\(= \cfrac{(x+y)^2-2xy+xy}{(x+y)^2-2xy-xy}\)
\(= \cfrac{(x+y)^2-xy}{(x+y)^2-3xy}\)
\(= \cfrac{(5)^2-1}{(5)^2-3\times 1}\)
\(= \cfrac{25-1}{25-3}\)
\(= \cfrac{24}{22}= \cfrac{12}{11}\)