1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I'm veryconfused with an a level maths q

  1. Apr 11, 2005 #1

    liz

    User Avatar

    the question:
    (im presuming n^2 means n squared)

    prove the following result: "a traingle with sides that can be written in the form n^2+1, n^2-1, and 2n (where n>1) is right angled.
    show, by means of a counter example, that the converse is false.

    this q was taken from the back of the book "the curious incedent of the dog in the night-time" and there was a full proof but i dont understand some of it.

    it start by exmplaining we need to prove which side is the longest by doing:

    n^2+1 - 2n = (n-1)^2

    if n>1 then (n-1)^2 >0

    therefore n^2+1 > 2n

    similarily (n^2+1) - (n^2-1) = 2

    therefore n^2+1 > n^2-1

    so n^2+1 > n^2-1.

    the rest is worked out using pythagoras but then the converse bit has completly lost me.

    if anyone would like to explain, then i would be very grateful. thanks!
     
  2. jcsd
  3. Apr 11, 2005 #2

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

    He is simply showing which side is longer,

    [tex](n^2+1) - (2n) = (n-1)^2[/tex]

    The left hand side is the difference between 2 of the sides.

    However, [itex](n-1)^2 \geq 0[/itex]

    So you can replace [itex](n-1)^2 [/itex] with: [itex]\geq 0[/itex] and you get:

    [tex](n^2+1) - (2n) \geq 0[/tex]

    Adding 2n to both sides:

    [tex]n^2+1 \geq 2n [/tex]

    So you know that the n2 + 1 side is greater or equal to the 2n side.
     
  4. Apr 11, 2005 #3

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Please,do not double post.It's not really fair.

    Daniel.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: I'm veryconfused with an a level maths q
  1. Math Q&A Game (Replies: 291)

  2. I'm illiterate in math! (Replies: 14)

Loading...