Login

Welcome, Guest. Please login or register.

March 29, 2024, 12:32:04 pm

Author Topic: Recreational Problems (MM level)  (Read 19686 times)  Share 

0 Members and 1 Guest are viewing this topic.

Flaming_Arrow

  • Victorian
  • ATAR Notes Superstar
  • ******
  • Posts: 2506
  • Respect: +16
Recreational Problems (MM level)
« on: June 12, 2008, 09:33:08 pm »
0
btw im in yr 11 so this is question from unit 1 and 2 book

ill start off




« Last Edit: June 12, 2008, 10:55:49 pm by chathuranj »
2010: Commerce @ UoM

Ahmad

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1296
  • *dreamy sigh*
  • Respect: +15
Recreational Problems (MM level)
« Reply #1 on: June 12, 2008, 09:46:08 pm »
0
Stickied!
Mandark: Please, oh please, set me up on a date with that golden-haired angel who graces our undeserving school with her infinite beauty!

The collage of ideas. The music of reason. The poetry of thought. The canvas of logic.


AppleXY

  • Life cannot be Delta Hedged.
  • Victorian
  • ATAR Notes Superstar
  • ******
  • Posts: 2619
  • Even when the bears bite, confidence never dies.
  • Respect: +16
Recreational Problems (MM level)
« Reply #2 on: June 12, 2008, 09:59:15 pm »
0
uhm? Ok.... it's not hard lol.

solve for x and sub in.









sub in to



etc etc,

x = 79 for +ve and -ve :)


MOD EDIT: prav you need to use "\frac" and "\sqrt", and +- is "\pm" :)
« Last Edit: June 12, 2008, 10:10:52 pm by AppleXY »

2009 - BBus (Econometrics/Economics&Fin) @ Monash


For Email: click here

Need a question answered? Merspi it!

[quote="Benjamin F

unknown id

  • Victorian
  • Trendsetter
  • **
  • Posts: 131
  • Respect: +1
Recreational Problems (MM level)
« Reply #3 on: June 12, 2008, 10:10:48 pm »
0






VCE Outline:
2007:   Accounting [48]

2008:   English [44], Maths Methods [50], Specialist Maths [41], Chemistry [50], Physics [44]

ENTER: 99.70





Flaming_Arrow

  • Victorian
  • ATAR Notes Superstar
  • ******
  • Posts: 2506
  • Respect: +16
Recreational Problems (MM level)
« Reply #4 on: June 12, 2008, 10:56:19 pm »
0
yep solved by applexy and unknown id
2010: Commerce @ UoM

Flaming_Arrow

  • Victorian
  • ATAR Notes Superstar
  • ******
  • Posts: 2506
  • Respect: +16
Recreational Problems (MM level)
« Reply #5 on: June 14, 2008, 11:36:34 am »
0
come on guys post some questions  :-[
2010: Commerce @ UoM

Ahmad

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1296
  • *dreamy sigh*
  • Respect: +15
Recreational Problems (MM level)
« Reply #6 on: June 14, 2008, 12:32:52 pm »
0
Show that for is never the square of an integer.
Mandark: Please, oh please, set me up on a date with that golden-haired angel who graces our undeserving school with her infinite beauty!

The collage of ideas. The music of reason. The poetry of thought. The canvas of logic.


Mao

  • CH41RMN
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 9181
  • Respect: +390
  • School: Kambrya College
  • School Grad Year: 2008
Recreational Problems (MM level)
« Reply #7 on: June 14, 2008, 12:48:54 pm »
0
Show that for is never the square of an integer.

[IGNORE ALL THIS, COMPLETELY WRONG :P ]

in order for this to be a square, this function need to be able to be represented as for a particular value of n

initial factorising gives



cannot be further factorised [without going into imaginary, hence for that expression to represent a square of an integer,

, NOT a positive integer.

hence, for , is never the square of an integer
« Last Edit: June 14, 2008, 07:00:11 pm by Mao »
Editor for ATARNotes Chemistry study guides.

VCE 2008 | Monash BSc (Chem., Appl. Math.) 2009-2011 | UoM BScHon (Chem.) 2012 | UoM PhD (Chem.) 2013-2015

Ahmad

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1296
  • *dreamy sigh*
  • Respect: +15
Recreational Problems (MM level)
« Reply #8 on: June 14, 2008, 12:56:13 pm »
0
Hmm, Mao, cannot be expressed as (without leaving the integers) yet it is a square when .

If you prove that an expression cannot be expressed as a square, it means it can not be a square for every x. But it's still possible that it's a square for a particular value of x.



I also thought I'd add 1 more problem,

Let be the familiar fibonacci numbers (with ).

Find

Back to chemistry study for me :P
Mandark: Please, oh please, set me up on a date with that golden-haired angel who graces our undeserving school with her infinite beauty!

The collage of ideas. The music of reason. The poetry of thought. The canvas of logic.


Neobeo

  • Victorian
  • Trendsetter
  • **
  • Posts: 188
  • 反逆 の Neobeo
  • Respect: +3
Recreational Problems (MM level)
« Reply #9 on: June 14, 2008, 01:15:14 pm »
0
Let be the familiar fibonacci numbers (with ).

Find

Let

Then


Giving us


Also




I should come up with a new problem shortly. But study comes first!
Mathematics Coach: Tuition and Enrichment // Email/MSN:

If you remember the flying birds, they died D=

bigtick

  • Victorian
  • Trendsetter
  • **
  • Posts: 152
  • Respect: +1
Recreational Problems (MM level)
« Reply #10 on: June 14, 2008, 05:39:36 pm »
0
=(n^2+an+1)^2, no rational a will satisfy
« Last Edit: June 14, 2008, 05:42:48 pm by bigtick »

Mao

  • CH41RMN
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 9181
  • Respect: +390
  • School: Kambrya College
  • School Grad Year: 2008
Recreational Problems (MM level)
« Reply #11 on: June 14, 2008, 06:20:15 pm »
0
Hmm, Mao, cannot be expressed as (without leaving the integers) yet it is a square when .

If you prove that an expression cannot be expressed as a square, it means it can not be a square for every x. But it's still possible that it's a square for a particular value of x.


but i did try to prove for a particular value of n! :P

[my basic principle is, if it is a perfect square for a particular value of n, then at some point it must be able to be expressed as a perfect square]

that is, at some point, , which is false for integer values of n.
« Last Edit: June 14, 2008, 06:23:48 pm by Mao »
Editor for ATARNotes Chemistry study guides.

VCE 2008 | Monash BSc (Chem., Appl. Math.) 2009-2011 | UoM BScHon (Chem.) 2012 | UoM PhD (Chem.) 2013-2015

Neobeo

  • Victorian
  • Trendsetter
  • **
  • Posts: 188
  • 反逆 の Neobeo
  • Respect: +3
Recreational Problems (MM level)
« Reply #12 on: June 14, 2008, 06:24:37 pm »
0
, NOT a positive integer.

You don't necessarily have to multiply two equal numbers to get a square.
Mathematics Coach: Tuition and Enrichment // Email/MSN:

If you remember the flying birds, they died D=

Mao

  • CH41RMN
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 9181
  • Respect: +390
  • School: Kambrya College
  • School Grad Year: 2008
Recreational Problems (MM level)
« Reply #13 on: June 14, 2008, 07:07:34 pm »
0
IN HINDSIGHT (thanks to dcc):



let this be a perfect square:



where k is an integer

hence, we must require to be rational.

but if we look at , , with the difference between the terms increasing. hence will not be a perfect square for the designated set of n, and will be irrational for

hence, it cannot be a perfect square


[i think that's what dcc meant :P ]
Editor for ATARNotes Chemistry study guides.

VCE 2008 | Monash BSc (Chem., Appl. Math.) 2009-2011 | UoM BScHon (Chem.) 2012 | UoM PhD (Chem.) 2013-2015

Mao

  • CH41RMN
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 9181
  • Respect: +390
  • School: Kambrya College
  • School Grad Year: 2008
Recreational Problems (MM level)
« Reply #14 on: June 14, 2008, 07:19:42 pm »
0


find such that the above system has non-zero solutions for
Editor for ATARNotes Chemistry study guides.

VCE 2008 | Monash BSc (Chem., Appl. Math.) 2009-2011 | UoM BScHon (Chem.) 2012 | UoM PhD (Chem.) 2013-2015