proof of that one rational solution to a quadratic implies another
For my proof, I'm hypothesizing that is the solution that is known to be rational.
Prove that if one solution for a quadratic equation of the form
is rational (where
are rational), then the other solution is also rational. (Use the fact that if the solutions of the equation are
So the rationals are closed under multiplication, addition and subtraction (and division, with nonzero divisors.) If is rational, then that closure ensures a rational , but isn't necessarily rational. I know I'm missing something, but I've been doing math all day and I'm a little brain-burned. Can anyone nudge me past the whole non-rational hurdle?