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Two infinite nested radicals are defined as follows. The first is x = sqrt(15 + 2*sqrt(15 + 2*sqrt(15 +...))), and the second is y = sqrt(2*sqrt(2*sqrt(2*...))). Which of the following statements is correct?

1. Both x and y are odd integers
2. Both x and y are prime numbers
3. x + y is not a prime number
4. x divided by y is an integer

Correct answer: Both x and y are prime numbers

Solution

Solving x² - 2x - 15 = 0 gives x = 5 (taking positive root), and y² = 2y gives y = 2. Both 5 and 2 are prime numbers.

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