Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#51 2015-05-06 05:37:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: 21 Questions from Amrita

Last 2 lines of the proof.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#52 2015-05-06 11:46:53

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

Nothing fishy there


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#53 2015-05-06 12:30:46

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: 21 Questions from Amrita

You understand differences?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#54 2015-05-06 19:45:56

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

2x?

I do not know what is wrong but please enlighten me


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#55 2015-05-07 03:35:10

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: 21 Questions from Amrita

Agnishom wrote:

You need to convince me that they are the only roots

Doesn't post 10 show this?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#56 2015-05-07 09:31:58

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: 21 Questions from Amrita

I do not know what is wrong but please enlighten me

There is nothing wrong, I was asking if you have seen or used the difference calculus before.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#57 2015-05-07 11:52:34

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

I haven't used it.

@bob: I do not get it.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#58 2015-05-07 12:28:12

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: 21 Questions from Amrita

If a quadratic has roots of a and b, it means that (x-a) and (x-b) are factors of that quadratic. Conversely, if you have the factors ( x - a ) and ( x - b ) then c can not be a root because ( x - c ) is not a factor unless c = a or c = b.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#59 2015-05-07 12:29:59

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

So, I will post a new question


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#60 2015-05-07 12:37:55

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

3) If the p-th, q-th, r-th, s-th terms of an Arithmetic progression are in Geometric Progression, show that (p-q), (q-r), (r-s) are in Geometric Progression

Last edited by Agnishom (2015-05-07 12:39:08)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#61 2015-05-07 19:16:32

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: 21 Questions from Amrita

hi Agnishom,

If you write

a + (p-1)d = r[a + (q-1)d]  and two more similar, and then subtract you get

d[(p-1) - (q-1)] = rd[(q-1) - (r-1)]  and so on.

All you need to do is simplify this.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

#62 2015-05-09 12:47:50

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

Thanks, the last time I checked, it worked


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#63 2015-05-09 13:38:38

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

Agnishom wrote:
AmritaR wrote:

If

25(9x^2 + y^2) + 9z^2 - 15(5xy + yz + 3xz) = 0

Prove that x,y,z form an AP


Proof:


25(9x^2 + y^2) + 9z^2 - 15(5xy + yz + 3xz) = 0

or, 225 x^2 + 25 y^2 + 9 z^2 - 75 x y - 15 y z - 45 x z = 0

or, (225 x^2 + 25 y^2 + 9 z^2 - 75 x y - 15 y z - 45 x z) + (225 x^2 + 25 y^2 + 9 z^2 - 75 x y - 15 y z - 45 x z) = 0 [Multiplying both sides by 2]

or, (225 x^2 - 75 x y - 75 x y + 25 y^2) + (25 y^2 - 15 y z - 15 y z + 9 z^2) + (9 z^2 - 45 x z - 45 x z + 225 x^2) = 0 [Rearrangement]

or, (15 x - 5 y)^2 + (5 y - 3 z)^2 + (3 z - 15 x)^2 = 0 (A)

But, by the trivial inequality:

(15 x - 5 y)^2, (5 y - 3 z)^2, (3 z - 15 x)^2 >= 0 (B)

From (A) and (B):

(15 x - 5 y)^2, (5 y - 3 z)^2, (3 z - 15 x)^2 = 0

Solving, we get:

(x, y, z) = (x, 3x, 5x)

Hence: x, y, z are in Arithmetic Progression.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#64 2015-05-09 14:33:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: 21 Questions from Amrita

You think that one is easier than mine?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#65 2015-05-09 18:54:25

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

Easy to understand? Yes


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#66 2015-05-09 20:42:59

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: 21 Questions from Amrita

Hmmm, I like mine better.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#67 2015-05-09 23:53:36

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

Why? It looks like gibberish


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#68 2015-05-10 07:26:47

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: 21 Questions from Amrita

Hmmm, looks can be deceiving.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#69 2015-05-10 11:45:35

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

Yep, I use that bobbym quote all the time.

Alokananda and I were waiting in the bus stop.
Me: Isn't that the bus you were looking for?
Alokananda: It looks so.
Me: but wait, looks can be deceiving


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#70 2015-05-10 15:47:21

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: 21 Questions from Amrita

Where were you going?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#71 2015-05-10 20:31:33

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

Going home


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#72 2015-05-10 21:23:27

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: 21 Questions from Amrita

Where were you coming from?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#73 2015-05-10 22:07:51

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

The school


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#74 2015-05-10 22:24:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: 21 Questions from Amrita

You wait for the bus together?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#75 2015-05-10 22:28:58

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: 21 Questions from Amrita

yes.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

Board footer

Powered by FluxBB