This problem comes from the 2006 British Maths Olympiad Round 2.

Find the minimum possible value of x^2 + y^2 given that x and y are real numbers satisfying
xy(x^2 − y^2) = x^2 + y^2 and x =/= 0.

This is a 3½-hour paper with 4 problems, taken by students in their own schools. Based on performances in BMO 1, up to 100 students (who are eligible to represent the UK at the IMO) are invited to sit BMO 2. Marking is carried out by around ten people, under the direction of the current IMO Team Leader. Especially elegant solutions may be awarded the Christopher Bradley elegance prize.

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Maths videos by Giuliano Grasso - mathematics graduate from the University of East Anglia.

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