Turn on thread page Beta

FP3 Group Question watch

    • Thread Starter

    H denotes the set of numbers of the form a + b 5, where a and b are rational. The numbers are
    combined under multiplication.
    (i) Show that the product of any two members of H is a member of H .
    It is now given that, for a and b not both zero, H forms a group under multiplication.
    (ii) State the identity element of the group.

    (iii) Find the inverse of a + b 5.
    (iv) With reference to your answer to part (iii), state a property of the number 5 which ensures that
    every number in the group has an inverse.
    I'm stuck on part iv). The answer says that it is because 5 is prime or sqrt5 is irrational, however I'm not sure why this is relevant.

    (The answer to part (iii) was a/(a^2-5b^2) - (b/(a^2-5b^2))sqrt5 )


    Notice that there is always an inverse if the denominators in the expression  \dfrac{a}{a^2-5b^2} - \dfrac{b}{a^2-5b^2} \sqrt{5} are not zero; but why can't  a^2-5b^2 equal zero?, with  a, b \in \mathbb{Q}.
Submit reply
Turn on thread page Beta
Updated: May 23, 2010

University open days

  • University of East Anglia
    All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
    Wed, 30 Jan '19
  • Aston University
    Postgraduate Open Day Postgraduate
    Wed, 30 Jan '19
  • Solent University
    Careers in maritime Undergraduate
    Sat, 2 Feb '19
Brexit: Given the chance now, would you vote leave or remain?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way


Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.