How to Solve This Radical Problem ? | Math Olympiad Questions

How to Solve This Radical Problem ? | Math Olympiad Questions

[@cosmolbfu67]

[(√5 -1)/2)]^8 . [((√5-1)/2))^2 +1]
=[(√5 -1)/2)]^8 .[√5(√5 -1)/2]
=√5[(√5 -1)/2]^9
=√5{[(√5 -1)/2]^3}^3
=√5{√5 -2}^3
=√5{17√5 -38}
=85-38√5 ***