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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 199

There was a question asking me to find at least one pair of numbers that have a product which is twice their sum? I had no idea how to do it. I was using trial and error but gave up after 5 minutes. I wrote this.

xy = 2(x+y)

xy

------ = 2 but this is only to check if the values work and doesn't really help me figure out which numbers I need.

(x+y)

*Last edited by PatternMan (2014-04-01 01:40:42)*

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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Lets assume

is 1 or prime. Then it divides 2 or .(i)

divides 2 or or . So .(ii)

divides . For this to be an integer, . So . So which is the same as (i) above.So

if is 1 or prime. There are other solutions if is not 1 and not prime but as you are not told to find them all, I think Ill stop here.*Last edited by Nehushtan (2014-04-01 02:23:29)*

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

Hi;

y = 0 and x = 0 is one obvious answer and there are an infinite number more.

y = 1 and x = - 2 for instance but your question only requires 1 pair.

Oh, sorry did not see the earlier solution. We were posting at the same time and Nehushtan was quicker. Me olde hands and eyes slow have they become, yes.

**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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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 199

xD You guys make me feel stupid lol. I thought of 0 0 but thought they wouldn't accept it because it doesn't look like twice the amount but there is no amount so twice nothing is nothing or whatever. I am just used to avoiding operations using 0.

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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

Hi;

Leaving 0 out is likely to make it feel lonely. It is just as good as any other number. Just do not divide by it.

**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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

In any problem where you are given a bivariate (consisting of two variables) equation and looking for ordered pairs which satisfy the equation, just solve for one variable in terms of the other and plug in values for one of the variables (it's easier if you plug in values for the variable you didn't solve for).

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,354

Got your report. Thanks. This is the second username I've banned in 24 hours. Look the same. Need to check the IP.

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

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

You banned him/her faster then the Microsoft people - he has been posting this there for the past two years on the Microsoft forums.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,354

Different name and IP, but much overlap in content so it seems to be the same guy.

I'll alert bobbym.

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

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PatternMan wrote:

There was a question asking me to find at least one pair of numbers

What sort of numbers? Integers? Naturals? Reals? Complex numbers?? What?

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'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

I presume he meant integers, since reals wouldn't take much work to find.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 199

For the two number,

the product is double the sum.

Work out the number I could be thinking of.

Give both possible pairs of answers.

I don't really fully understand it myselv but this is the solution I was given.

x(x+7.5) = 2(x+x+7.5)

x^2 + 7.5x = 2(2x +7.5)

x^2 + 7.5x = 4x + 15

x^2 + 3.5x - 15 = 0

2x^2 + 7x - 30 = 0

(2x - 5) (x + b) = 0

2x -5 = 0 or x + b = 0

x = 5/2, x = -b

2.5+7.5 = 10, -6 + 7.5= 1.5

answer 2.5 and 10

or

-6 and 1.5

*Last edited by PatternMan (2014-04-02 02:00:10)*

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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

Hi PatternMan;

Who gave you that solution?

**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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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 199

bobbym wrote:

Hi PatternMan;

Who gave you that solution?

The question was an A* question from an exam paper for 16 year olds. I got a spreadsheet with the solutions to the problems. That is the solution they gave that would yeild full marks.

*Last edited by PatternMan (2014-04-02 06:05:35)*

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

That is a very bad solution in my opinion.

**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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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 199

bobbym wrote:

That is a very bad solution in my opinion.

Why do you think it's bad?

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

Because it acts as if those are the correct answers! They are not. They are 2 of the correct answers but what about the gazillions of others?

**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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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 199

bobbym wrote:

Because it acts as if those are the correct answers! They are not. They are 2 of the correct answers but what about the gazillions of others?

but couldn't you just substitute in different values where 7.5 is?

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

Hi;

Yes, you could. I meant the top of page: "Give both possible pairs of answers."

Should be, "give one possible pair of answers."

But maybe that is nitpicking.

**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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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 199

bobbym wrote:

Hi;

Yes, you could. I meant the top of page: "Give both possible pairs of answers."

Should be, "give one possible pair of answers."

But maybe that is nitpicking.

No I agree with you. Lots of questions in the school curriculum over here try to pigeonhole you. They ask closed questions to open answers, and ask open questions but only want a selection of answers. Both implies there are only 2 possible.

*Last edited by PatternMan (2014-04-02 08:35:20)*

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

I think that's a very stupid thing to do. Math is hard enough - you don't have to confuse the students by wording the question is a wrong way.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 199

I sometimes think it is done intentionally. Many questions are oversimplified which makes them plain wrong and hard to follow for the rational person. I easily find fault and have difficulty understanding some questions. I feel like it's conditioning. The students thought process when seeing a question becomes "if questioin = a : use b formula, else: end program." Then anything outside of that people will have no idea what to do. A lady yesterday told me that math is just knowing which formulas to use. Now imagine a student had that education and belief, and actually wanted to pursue math at university.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

Tell that lady to first know what she is talking about. Now, if she had said "high school math is just knowing which formulas to use", I would agree with her.

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

A lady yesterday told me that math is just knowing which formulas to use. Now imagine a student had that education and belief,

Do not get mad and I know there will be much cyber guava thrown at me by the purists but I have never seen anything that humans are capable of doing well that did not come down to knowing a couple of dozen to several hundred rules.

**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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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 199

bobbym wrote:

A lady yesterday told me that math is just knowing which formulas to use. Now imagine a student had that education and belief,

Do not get mad and I know there will be much cyber guava thrown at me by the purists but I have never seen anything that humans are capable of doing well that did not come down to knowing a couple of dozen to several hundred rules.

Can you remember all those rules and apply them correctly? The problem is it doesn't make you any good at mathematics. You'll look at the rules and they'll be devoid of any meaning to you. You just follow them as a means to an end. When a rule doesn't work you'll have no idea what to do. Learning formulas wont help much when you need to figure out relationships and patterns to solve problems.

In simple terms.... Justin Beiber can learn the algorithm to solve a rubiks cube but he would never figure out howw to solve a 4 or 5 sided one just by being able to follow the procedure.

I personally have bad memory and remember concepts way better than rules. I forget meaningless information. Hey I can go to the kitchen and just get 6 apples. Hey I can split these into 3 and 3, 1 and 5, 2 and 4. Hey it doesn't matter which way I put them together you always get 6 back. "Commutative law," If I split them into equal parts I get 2 groups of 3 or 3 groups of 2 or 1 group of 6 originally. Hey those are factors and what I just did is what they call division. - much more intuitive no?...

*Last edited by PatternMan (2014-04-02 09:38:11)*

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