Contradiction in Assuming a Rational Root for x^2 – 2 = 0
Consider the quadratic equation \(x^2 – 2 = 0\). Assume that there exists a rational root \(x = \frac{p}{q}\) where \(p\) and \(q\) are integers with no common factors (i.e., the fraction is in lowest terms). (a) Begin by substituting \(x = \frac{p}{q}\) into the equation and deduce a necessary condition on \(p\) (i.e., show […]