Problem #PRU-64622

Problems Algebra Polynomials Algebraic identities for polynomials Identical transformations Geometry Plane geometry Quadrilateral Inscribed quadrilaterals

13–15 3.0

Problem

The number $x$ is such a number that exactly one of the four numbers $a = x - \sqrt{2}$ , $b = x - 1 / x$ , $c = x + 1 / x$ , $d = x^{2} + 2 \sqrt{2}$ is not an integer. Find all such $x$ .

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