MathDB

16

Part of 1999 National Olympiad First Round

Problems(1)

Rational roots

Source: 0

4/21/2009
How many pairs of rational number (x,y) \left(x,y\right) are there satisfying the equation y \equal{} \sqrt {x^{2} \plus{} \frac {1}{1999} }?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> Infinitely many<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}