Question

if x = root 5 + root 3 whole upon root 5 minus root 3 and Y equal root 5 minus root 3 whole upon root 5 + root 3 then X + Y + xy =​

Answer 1

Please see the attachment

Answer 2

if
$x = \frac{ \sqrt{5 } + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$
if
$y = \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$
then
$x + y + xy = ( \: \: \: )$
put the value of x and y
$= x + y + xy \\ = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } + \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } + \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$
Connection of demonemeter and x×y=1
$= \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } + \frac{ \sqrt{5 } - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ = \frac{5 - 3}{ {( \sqrt{5} - \sqrt{3)} }^{2} } + \frac{5 - 3}{ {( \sqrt{5} + \sqrt{3)} }^{2} } \\ = \frac{2}{5 - 2( \sqrt{5)} ( \sqrt{3)} +3} + \frac{2}{5 +2( \sqrt{5)}( \sqrt{3)} + 3 } \\ = \frac{2}{8 - 2 \sqrt{15} } + \frac{2}{8 + 2\sqrt{15} } \\ = \frac{4}{6 \sqrt{15} }$