Exams › SSC CGL (Prelims) › General

Evaluate the infinite nested radical x = sqrt(15 + sqrt(15 + sqrt(15 + ...))).

1. 3
2. 2
3. (1 + sqrt(61))/2
4. 4

Correct answer: (1 + sqrt(61))/2

Solution

Setting x = sqrt(15 + x) gives x^2 - x - 15 = 0. The positive root is x = (1 + sqrt(61))/2, since 15 is not of the form n(n-1) that yields an integer.

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