​ If x = √5 + √3/√5 - √3 and y = √5 - √3/√5 + √3 , then x + y + xy = A. 9 B. 5 C. 17 D. 7 ​

Question

If x = \(\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3}\) and y = \(\frac{\sqrt5-\sqrt3}{\sqrt5+\sqrt3}\), then x + y + xy =

A. 9

B. 5

C. 17

D. 7

Answer 1

Given x = √5 +√3/√5 -√3, y =√5 - √3/√5 +√3

= xy = 4² - √15² = 16 – 15 = 1

So,

x + y+ xy = 4+√15 + 4 - √15 + 1 = 9.