Maths Olympiad Exam

Solve the following equation for real x:
(x^2 + x - 2)^3 + (2x^2 - x - 1)^3 = 27(x^2 - 1)^3

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Maths Olympiad Other Question

In an acute triangle ABC, points D, E, F are located on the sides BC, CA, AB respectively
such that
CD*CE=CA*CB, AE*AF=AB*AC, BF*BD=BC*BA.
Prove that AD, BE, CF are the altitudes of ABC. Let a, b, c be positive integers such that a divides b^2, b divides c^2 and c divides a^2. Prove that abc divides (a + b + c)^7.