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Conclusion From a Relation

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June 8, 2009
inequalitiesGaussquadratics

Problem Statement

If two real numbers x x and y y satisfy the equation \frac{x}{y} \equal{} x \minus{} y, then: <spanclass=′latex−bold′>(A)</span> x≥4 and x≤0<spanclass=′latex−bold′>(B)</span> y can equal 1<spanclass=′latex−bold′>(C)</span> both x and y must be irrational<spanclass=′latex−bold′>(D)</span> x and y cannot both be integers<spanclass=′latex−bold′>(E)</span> both x and y must be rational <span class='latex-bold'>(A)</span>\ {x \ge 4}\text{ and }{x \le 0}\qquad \\ <span class='latex-bold'>(B)</span>\ {y}\text{ can equal }{1}\qquad \\ <span class='latex-bold'>(C)</span>\ \text{both }{x}\text{ and }{y}\text{ must be irrational}\qquad \\ <span class='latex-bold'>(D)</span>\ {x}\text{ and }{y}\text{ cannot both be integers}\qquad \\ <span class='latex-bold'>(E)</span>\ \text{both }{x}\text{ and }{y}\text{ must be rational}
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