maths Maths Puzzle

Find all positive real numbers x such that both root x + 1/root x and cube root of x + 1/cube root of x are integers.

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maths Other Question

The minute hand of a clock is twice as long as the hour hand. At what time, between 00:00 and when the hands are next aligned (just after 01:05), is the distance between the tips of the hands increasing at its greatest rate? The smallest distance between any two of six towns is m miles. The largest distance between any two of the towns is M miles. Show that M/m greater than or equal to root 3. Assume the land is flat.