Prove that if x is rational and y irrational then 3y-x is irrational. (Hint: use contra-diction!?
- Anonymous3 years agoFavourite answer
Suppose 3y - x is rational, = p/q say. So 3y = x + p/q = a/b + p/q (setting x = a/b) = (aq + bp)/(pq) = integer/integer → y = integer/(3 x integer) = integer/integer = rational number. Contradicts hypothesis that y is irrathional. Thus our supposition that 3x - y is rational is false and 3x - y is irrational.