Latest Maths Olympiad Aptitude Question SOLUTION: Show that the equation x^2 + y^2 + z^2 = (x - y)(y - z)(z - x) has infinitely many solutions in integers x, y, z.

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Previous Question: Let ABC be a triangle in which no angle is 90◦. For any point P in the plane of the triangle, let A1,B1,C1 denote the reflections of P in the sides BC,CA,AB respectively. Prove the following statements: (a) If P is the incentre or an excentre of ABC, then P is the circumcentre of A1B1C1; (b) If P is the circumcentre of ABC, then P is the orthocentre of A1B1C1; (c) If P is the orthocentre of ABC, then P is either the incentre or an excentre of A1B1C1. Next Question: If a, b, c are positive real numbers such that abc = 1, prove that ab+c bc+a ca+b ≤ 1.

(#M40021936) MATHS OLYMPIAD question ALGEBRA Keep an EYE

Show that the equation
x^2 + y^2 + z^2 = (x - y)(y - z)(z - x)
has infinitely many solutions in integers x, y, z.: Asked In Maths Olympiad MAN (10 years ago); Unsolved; Is this Puzzle helpful? (0) (0) Submit Your Solution

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Previous Question: Let ABC be a triangle in which no angle is 90◦. For any point P in the plane of the triangle, let A1,B1,C1 denote the reflections of P in the sides BC,CA,AB respectively. Prove the following statements: (a) If P is the incentre or an excentre of ABC, then P is the circumcentre of A1B1C1; (b) If P is the circumcentre of ABC, then P is the orthocentre of A1B1C1; (c) If P is the orthocentre of ABC, then P is either the incentre or an excentre of A1B1C1. Next Question: If a, b, c are positive real numbers such that abc = 1, prove that ab+c bc+a ca+b ≤ 1.

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