Help with Number Systems - Year 1
I am stuck on the question 'Show that there are irrational numbers a and b such that both a + b and ab are rational.'
Obviously I'm not looking for someone to tell me the answer, but I have no idea where to even start with this, so a few starting pointers would be helpful?
Obviously I'm not looking for someone to tell me the answer, but I have no idea where to even start with this, so a few starting pointers would be helpful?
Think of something that will satisfy the sum first. The product seems to be more natural. To get rid of the irrational number you need to cancel it with something..
Original post by RyanAGTerry
I am stuck on the question 'Show that there are irrational numbers a and b such that both a + b and ab are rational.'
Obviously I'm not looking for someone to tell me the answer, but I have no idea where to even start with this, so a few starting pointers would be helpful?
Obviously I'm not looking for someone to tell me the answer, but I have no idea where to even start with this, so a few starting pointers would be helpful?
Something that may be a starting idea to try and find a and b given a + b and ab.
You may have seen what I'm thinking of or not at (FM) A-level.
Spoiler
Trial and error should give you an example eventually as well. You should then think why what you did worked, and how it could be generalised.
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