Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    "express the following in the form a+b root 5, where a and b are constants"
    how do i apply this question to these 4 questions...
    (2+root5)squared
    (3-2root5)squared
    1 over root 5 + 1
    1+ root 5 over 2- root 5
    ASAP
    • Peer Support Volunteers
    • Study Helper
    Offline

    19
    Peer Support Volunteers
    Study Helper
    (Original post by caitlindavies)
    "express the following in the form a+b root 5, where a and b are constants"
    how do i apply this question to these 4 questions...
    (2+root5)squared
    (3-2root5)squared
    1 over root 5 + 1
    1+ root 5 over 2- root 5
    ASAP
    What have you done/tried so far?

    You need to expand the first two and rationalise the denominator for the last two.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by usycool1)
    What have you done/tried so far?

    You need to expand the first two and rationalise the denominator for the last two.
    i havent done anything so far, i just dont understand what it means by a and b are constants
    • Peer Support Volunteers
    • Study Helper
    Offline

    19
    Peer Support Volunteers
    Study Helper
    (Original post by caitlindavies)
    i havent done anything so far, i just dont understand what it means by a and b are constants
    a and b are constants (i.e. non changing values, basically a number in each case) that you need to work out.
    • Study Helper
    Offline

    16
    ReputationRep:
    Study Helper
    (Original post by caitlindavies)
    i havent done anything so far, i just dont understand what it means by a and b are constants
    It means that whatever you work out the answer to be in each case, it will look like

    a + b\sqrt{5}

    where a and b are some 'ordinary' numbers (not surds) that you have to work out for yourself.
    Offline

    18
    ReputationRep:
    (Original post by caitlindavies)
    i havent done anything so far, i just dont understand what it means by a and b are constants
    Concrete example (which is intentionally not one of the expressions you've been asked to find):

    To express \dfrac{1}{3-\sqrt{5}} in the form a + b \sqrt{5}:

    \dfrac{1}{3-\sqrt{5}} = \dfrac{1}{3-\sqrt{5}} \dfrac{3+\sqrt{5}}{3+\sqrt{5}} = \dfrac{3+\sqrt{5}}{(3-\sqrt{5})(3+\sqrt{5})} = \dfrac{3+\sqrt{5}}{3^2 - \sqrt{5}^2}(treating the denominator as the difference of 2 squares)

     = \dfrac{3+\sqrt{5}}{9 - 5} = \dfrac{3+\sqrt{5}}{4} = \dfrac{3}{4} + \dfrac{1}{4}\sqrt{5}

    (This answers the question, with a = 3/4 and b = 1/4, but you don't actually need to state what a and b would be).
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: September 15, 2015
Poll
Cats or dogs?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

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