If x = √√(5 + 1)/√(5 - 1), then x2

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If x = √√(5 + 1)/√(5 - 1), then x² - x - 1 is equal to

1. 0
2. 1
3. 2
4. 5

Correct Option: A

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