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#1 2012-09-18 23:57:47

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

What must be added to the following expression to make it a perfect square?

'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.

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#2 2012-09-19 01:22:18

Sylvia104
Banned
Registered: 2011-09-19
Posts: 29

Let
.

Expanding,

.

Comparing coefficients gives

.

:

Last edited by Sylvia104 (2012-09-19 01:23:29)

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#3 2012-09-19 03:44:13

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
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Last edited by Agnishom (2012-09-19 03:45:47)

'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.

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#4 2012-09-19 04:14:07

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

Yeah!
I coudn't pay enough concentration.

Sometimes it happens

'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.

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#5 2012-09-19 05:30:31

Au101
Member
Registered: 2010-12-01
Posts: 353

Hi

Last edited by Au101 (2012-09-19 05:31:13)

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#6 2012-09-19 17:01:09

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

Thanks!

'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.

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#7 2012-09-19 19:01:39

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

Hi Agnishom;

There is another way which does not require any of the heavy machinery.

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.

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#8 2012-09-21 00:57:49

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

Really? Whazzit?

'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.

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#9 2012-09-21 01:04:21

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

Hi;

The method depends on inspection and some knowledge of common squares. I am only offering it as a sometime faster alternative. In most cases you should use and learn the method used in post #2.

Let b be what you have to add.

You are looking for a b in

You have 2 equations which say what b must be added to b + 56 and b + 200 that give you two squares. Well the next square after 56 is 64 so b = 8 is a possibility but 200 + 8 is not a square.

Then next square is 81 which means in b + 56 = 81 b would be 25. Plugging in b into the second equation 25 + 200 = 225 which is a square too. You are done, b = 25.

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.

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#10 2012-09-21 16:16:19

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,859
Website

I think #2 was better
It doesn't look very tedious except that I was a little bit confused then

'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.

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#11 2012-09-21 19:20:21

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