x = [(√5 + √3) / (√5 - √3)] * [(√5 + √3) / (√5 + √3)] = (√5 + √3)2 / (5 - 3) =(5 + 3 + 2√15) / 2 = 4 + √15.
y = [(√5 - √3) / (√5 + √3)] * [(√5 - √3) / (√5 - √3)] = (√5 - √3)2 / (5 - 3) =(5 + 3 - 2√15) / 2 = 4 - √15.
x2 + y2 = (4 + √15)2 + (4 - √15)2
= 2[(4)2 + (√15)2]
= 2 * 31
= 62.