If x = √ √(5 + 1)/√(5 - 1), then x 2 - x - 1 is equal to

Here, x = √√5 + 1/√5 - 1
On rationalising the terms given in square root, we get
x = √√5 + 1/√5 - 1 x √5 + 1/√5 + 1
√5 + 1/2
Now, substituting the value of x in x² - x - 1.
∴ x² - x - 1 = (√5 + 1/2)² - (√5 + 1/2) - 1
= 5 + 1 + 2√5/4 - √5 + 1/2 - 1
= 6 + 2√5 - 2√5 - 2 - 4 /4 = 0