The numbers 59, 53, 51, 43, 36, (8x + 1), (x^2 + 1), 13, 12, 9, 7, 3 are written in descending order and their median is 25. What is/are the values of x ?

Explanation

The median of 12 numbers is the average of the 6th and 7th terms. Thus, ((8x+1) + (x^2+1)) / 2 = 25, simplifying to x^2 + 8x - 48 = 0. The roots are x=4 and x=-12. Because the sequence must strictly descend, substituting x=-12 gives terms -95 and 145, breaking the order. For x=4, terms are 33 and 17, preserving descending order. Hence, x=4 only.

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