If x = (√3 + 1)/ (√3-1) and y = (√3 – 1)/(√3+1), then the value of (x2 + y2) is:

If x = (√3 + 1)/ (√3-1) and y = (√3 – 1)/(√3+1), then the value of (x² + y²) is:

A 10

B 13

C 14

D 15

Correct Answer: Option C

x = (√3 + 1)/( √3-1) x (√3 + 1)/ (√3+1)

=> x = ((√3 + 1)2)/(3-1)

=>x = (3 + 1 + 2√3)/2 = 2 + √3.

y =(√3 - 1) / (√3+1) x (√3 - 1)/( √3-1)

=> y = (√3 - 1)2/(3-1)

=> y = 3 + 1 - 2√3 = 2 - √3.

So, x2 + y2 = (2 + √3)2 + (2 - √3)2

= 2(4 + 3)

= 14