maths Maths Puzzle

If the equation x4 − x3 + x + 1 = 0 has roots a, b, c, d, show that 1/a + 1/b is a root of x6 + 3x5 + 3x4 + x3 − 5x2 − 5x − 2 = 0.

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maths Other Question

For how many integers n > 1 is x49 congruent to x (modulo n) true for all integers x? 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?