If x = \frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3} and xy = 1 then x + y =

TS ICET 2015 Question Paper with Solutions for online practice

Question : 89 of 200

Marks: +1, -0

If x =

{√5+√3}/{√5-√3}

and xy = 1 then x + y =

Solution:

Given

x={√5+√3}/{√5-√3}

and

y=1/x={√5-√3}/{√5+√3}

∴x+y={√{5}+√{3}}/{√{5}-√{3}}+{√{5}-√{3}}/{√{5}+√{3}}

={(√{5}+√{3})^{2}+(√{5}-√{3})^{2}}/{(√{5})^{2}-(√{3})^{2}}={2[(√{5})^{2}+(√{3})^{2}]}/{5-3}

={2×8}/{2}=8

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