help needed (maths)

My daughter has a question:

Prove that (n+5)-(n+3)squared = 4(n+4).

Any help appreciated .Thanks

I thought you were the intelligent one in the family stick.

My daughter has a question:

 

 

Prove that (n+5)-(n+3)squared = 4(n+4).

 

 

Any help appreciated .Thanks

I don't think it does, as it is written. Are you sure you've got it right?

PM Ludwig, he'll know.

I don't think it does, as it is written. Are you sure you've got it right?

Yes that is the question ,i`ve just checked. But i`m stuck i can`t prove it

Thanks guys.Just worked it out -it was a misprint.

Question should read prove (n+5) squared - (n+3) squared = 4(n+4)

Special thanks to whitey grandad for making me realise it was a misprint!

First draft.

n=2.

(2+5)sq -(2+3)sq = 24 = 4(2+4)

(49)-(25)=24= 4x6

Cool. I can also confirm the original question wasted 5 minutes of my life with no answer.

Thanks guys.Just worked it out -it was a misprint.

 

Question should read prove (n+5) squared - (n+3) squared = 4(n+4)

 

Special thanks to whitey grandad for making me realise it was a misprint!

Are you sure thats the question? As I think that only works out to be true when n is -4

Edit: think I'm wrong: (n+5)squared -(n+3)squared = 4(n+4) is true...

n = 0

n could equal anything I reckon.

(N+5)(N+5) - (N+3)(N+3) =

Nsqr +10N+25 - (Nsqr +6N+9) =

4N + 16 = 4 (N+4)

God i have too much time on my hands....

n could equal anything I reckon.

think you might be right.

Remember though that the question is to prove the rule.

Not find out the value of n.

Ah I remember learning this in school. I use the term 'learning' loosely. I still don't have bloody clue what they are or how to do them and I haven't had to use it since I left school. Me 1-0 School.

My daughter has a question:

 

 

Prove that (n+5)-(n+3)squared = 4(n+4).

 

 

Any help appreciated .Thanks

( (n+5) - (n+3) )^2 = Squaring something means times it by itself therefore...

( (n+5)*(n+5) ) - ( (n+3)*(n+3) ) = Now multiply out

(n^2 + 5n + 5n + 25) - ( n^2 + 3n + 3n + 9 ) = Simplify

(n^2 + 10n + 25) - ( n^2 + 6n + 9) = Subtract the values that match from each other

4n + 16 = Check what divides through both values

4(n+4)

think you might be right.

 

Remember though that the question is to prove the rule.

 

Not find out the value of n.

yep, I got it down to 4n + 16 = 4n + 16.

edit

nerd alert

N = Na, na, na, na, na, na, na, na, na, na, na baby give it up, give it up

N = Na, na, na, na, na, na, na, na, na, na, na baby give it up, give it up

Ra-si-ak, Ra-siak? Gregorz Rasiak?

think you might be right.

 

Remember though that the question is to prove the rule.

 

Not find out the value of n.

Something vaguely interesting involving a different method to the one used before would be to use inductive reasoning to show it is true for all n (though that wouldn't be expected at what appears to be GCSE level maths (it's not even in the A Level Maths syllabus, which is a little ridiculous)).

Essentially, if you show that the statement holds true for n=1, then demonstrate that if we accept that it holds for n=k then that implies that it would also hold for n=k+1, then it holds for all n. Because, from the reasoning followed, as it holds for 1, and holding for any 'k' implies it holds for 'k+1', it must hold for 2,3,4,5..... like a domino effect. Though, in this problem, you'd end up multiplying out to show that p(k) => p(k+1), so it's somewhat unnecessary in this situation, but interesting (and more rigorous) nonetheless.

+1

wooooooosh , reet over my head

Something vaguely interesting involving a different method to the one used before would be to use inductive reasoning to show it is true for all n (though that wouldn't be expected at what appears to be GCSE level maths (it's not even in the A Level Maths syllabus, which is a little ridiculous)).

 

Essentially, if you show that the statement holds true for n=1, then demonstrate that if we accept that it holds for n=k then that implies that it would also hold for n=k+1, then it holds for all n. Because, from the reasoning followed, as it holds for 1, and holding for any 'k' implies it holds for 'k+1', it must hold for 2,3,4,5..... like a domino effect. Though, in this problem, you'd end up multiplying out to show that p(k) => p(k+1), so it's somewhat unnecessary in this situation, but interesting (and more rigorous) nonetheless.

We covered Proof by Induction as the very first subject for A-level Pure Maths and it made we want to jack it in.

Why use letters? Isn't that what numbers are for? :confused:

Why use letters? Isn't that what numbers are for? :confused:

:smt069:rolleyes:

This is the difference of two squares rule:

a² - b² = (a+b)*(a-b)

Ra-si-ak, Ra-siak? Gregorz Rasiak?

Nope....

Na, na, na, na, na, na, na, na, na, na, na David Connolly, Connolly, David Connolly Na, na, na, na, na, na, na, na, na, na, na!

My daughter has her Gcse maths exam tomorrow.Thanks dark munster for providing some tuition :-)

( (n+5) - (n+3) )^2 = Squaring something means times it by itself therefore...

( (n+5)*(n+5) ) - ( (n+3)*(n+3) ) = Now multiply out

(n^2 + 5n + 5n + 25) - ( n^2 + 3n + 3n + 9 ) = Simplify

(n^2 + 10n + 25) - ( n^2 + 6n + 9) = Subtract the values that match from each other

4n + 16 = Check what divides through both values

4(n+4)

FAIL!

( (n+5) - (n+3) )^2

does not equal

( (n+5)*(n+5) ) - ( (n+3)*(n+3) )

it equals

(n+5)*(n+5) ) - (n+3)*(n+3) - 2 * (n+5) (n+3)

That wasn't the question.

Something vaguely interesting involving a different method to the one used before would be to use inductive reasoning to show it is true for all n (though that wouldn't be expected at what appears to be GCSE level maths (it's not even in the A Level Maths syllabus, which is a little ridiculous)).

 

Essentially, if you show that the statement holds true for n=1, then demonstrate that if we accept that it holds for n=k then that implies that it would also hold for n=k+1, then it holds for all n. Because, from the reasoning followed, as it holds for 1, and holding for any 'k' implies it holds for 'k+1', it must hold for 2,3,4,5..... like a domino effect. Though, in this problem, you'd end up multiplying out to show that p(k) => p(k+1), so it's somewhat unnecessary in this situation, but interesting (and more rigorous) nonetheless.

Not relevant here - you are just showing off. Also, this wouldn't be a satisfactory answer as you have only proved it for positive integers, not all real numbers, which would be impossible by induction.

(N+5)(N+5) - (N+3)(N+3) =

Nsqr +10N+25 - (Nsqr +6N+9) =

4N + 16 = 4 (N+4)

 

 

God i have too much time on my hands....

Correct

Not relevant here - you are just showing off. Also, this wouldn't be a satisfactory answer as you have only proved it for positive integers, not all real numbers, which would be impossible by induction.

fml