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#1 2012-09-19 21:57:47

Agnishom
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What must be added?

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'
'Who are you to judge everything?' -Alokananda

#2 2012-09-19 23:22:18

Sylvia104
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Re: What must be added?

Let
.

Expanding,
.

Comparing coefficients gives
.

Hence you must add
:

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

#3 2012-09-20 01:44:13

Agnishom
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Re: What must be added?

Please expain why you get

Last edited by Agnishom (2012-09-20 01:45:47)


'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'
'Who are you to judge everything?' -Alokananda

#4 2012-09-20 02:14:07

Agnishom
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Re: What must be added?

Yeah!
I coudn't pay enough concentration.
sad
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'
'Who are you to judge everything?' -Alokananda

#5 2012-09-20 03:30:31

Au101
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Re: What must be added?

Hi smile

Last edited by Au101 (2012-09-20 03:31:13)

#6 2012-09-20 15:01:09

Agnishom
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Re: What must be added?

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'
'Who are you to judge everything?' -Alokananda

#7 2012-09-20 17:01:39

bobbym
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Re: What must be added?

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#8 2012-09-21 22:57:49

Agnishom
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Re: What must be added?

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'
'Who are you to judge everything?' -Alokananda

#9 2012-09-21 23:04:21

bobbym
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Re: What must be added?

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



that makes a square. So start with





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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10 2012-09-22 14:16:19

Agnishom
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Re: What must be added?

I think #2 was better hmm
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'
'Who are you to judge everything?' -Alokananda

#11 2012-09-22 17:20:21

bobbym
Administrator

Online

Re: What must be added?

Okay, I just thought you might want to see something else.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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