maths Maths Puzzle

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.

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maths Other Question

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. Let a, b, n, and m be positive integers, with n > 1. Show that an + bn = 2m implies a = b.