Problem #PRU-64638

Problems Algebra Polynomials Algebraic identities for polynomials Identical transformations Calculus Real numbers Rational and irrational numbers

14–15 3.0

Problem

The numbers $x$ , $y$ and $z$ are such that all three numbers $x + y z$ , $y + z x$ and $z + x y$ are rational, and $x^{2} + y^{2} = 1$ . Prove that the number $x y z^{2}$ is also rational.

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