If a + 1/a = √3, find a⁶ + 1/a⁶

Find the value of: (1 - 1/2)(1 - 1/3)(1 - 1/4)...(1 - 1/n) where n > 1

If x = (√5 + 1)/(√5 - 1) and y = (√5 - 1)/(√5 + 1), find x² + y²

Simplify: √(5 + 2√6) + √(8 - 2√15)