Question

if x is rational and y is irrational then show that (x+y) is always irrational​

Answer 1

answer is Y

Step-by-step explanation:

x+y = p/q

therefore m/n + y = p/q

therefore y =p/q - m/n

Therefore y = np - mq / nq

also so y can be written in a fraction =Y is Rational

But we initially asserted that y was irrational and hence we have a contradiction, and so the sum x+y

cannot be rational and hence it must be irrational, QED.