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 and are rational), then the other solution is also rational. (Use the fact that if the solutions of the equation are and , then .
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?