Question

Find an example of two irrational numbers a and b for which a≠b and a/b is rational.

Answer 1

Yes.

Here’s an easy (and cheap) one:
`\\\\\sqrt 2\\-\sqrt 2`

In fact, I can find a formula for them.

The two numbers will always be of the form:

`x_1 =a+b\sqrt c \\x_2 =a-b\sqrt c \\`

A and B are rational

C is rational and not a perfect square of a rational number

These are irrational because the square root will not resolve to a rational number.

12=(+√)(−√)=2−(√)2=2−2 . Looks rational to me.

1+2=+√+−√=2 , which also is rational.

Hope this helped!