A is rational number x is irrational number prove a+x is irrational number

A is rational number x is irrational number prove a+x is irrational number

If a+x is not an irrational number, then a+x is a rational number.
And because a is a rational number, a+x is a rational number, so x is also a rational number, and the problem design contradiction, so the assumption is not true, the original proposition!

This is+x is not an irrational number, then a+x is a rational number.
And because a is a rational number, a+x is a rational number, so x is also a rational number, and the problem design contradiction, so the assumption is not true, the original proposition!

Let a be a rational number and x be an irrational number. It is proved that:(1) a+x is an irrational number;(2) when a is not zero, ax is an irrational number.

1) Any rational number can be expressed as: q/p, p, q are all integers; conversely, any number in the form of q/p is the same. a is a rational number, so a=q/p If a+x is a rational number, then: a+x=q'/p', x=q'/p'-a=q'/p'-q/p'=(p*q'-q*p')/(p*p') i.e. x=...