Solve for x:

If the 10^th term of an A.P. is 52 and 17^th term is 20 more than the 13^th term, find the A.P.

If the roots of the equation (c² – ab)x² – 2(a² – bc)x + b² – ac = 0 in x are equal, then show either a = 0 or a³ + b³ + c³ = 3abc.

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train.

A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30° to 45° in 12 minutes, find the time taken by the car now to reach the tower.