• Support PF! Buy your school textbooks, materials and every day products Here!

2 questions please

  • #1
hi, I have 2 questions here that I am stuck on. I thought I may as well stick them in the same topic to avoid cluttering the forum. hope you can help, thnx

QUESTION 1

Homework Statement



Fred invests an amount of money in an account paying r% compound interest per annum. The amount of money doubles after n years.

Find a formula for r in terms of n.

Homework Equations





The Attempt at a Solution



where m is the initial money]

[tex]2m = m(\frac{100+r}{100})^{n}[/tex]

[tex]2 = (\frac{100+r}{100})^{n}[/tex]

[tex]\sqrt[n]{2} = \frac{100+r}{100}[/tex]

[tex]100\sqrt[n]{2} = 100 + r[/tex]

[tex]r = 100\sqrt[n]{2} - 100[/tex]

now, that seems to be the right answer but looks kinda ugly... first of all, is that answer right? and secondly, if so, is there a nicer way to put it :S ?

thnx


QUESTION 2

Homework Statement



Using this result, or otherwise

I proved for the previous question that

[tex](m^2+1)(n^2+1) = (m + n)^2 + (mn -1)^2[/tex]


write 500050 as the sum of 2 square numbers.

Homework Equations





The Attempt at a Solution



I havn't been told how to do this. maybe because this is on a past paper it isn't on the syllabus anymore, but still, I'd like to know how to do it because i doubt its that hard once you know how.

thnx
 
Last edited:

Answers and Replies

  • #2
correction:

the latex thing wont let me change it despite me trying a billion times. so basically, in the first use of latex the star thing isnt supposed to be there.

if mod or whatever can figure out how to remove the star, please do :D thnx
 
  • #3
Dick
Science Advisor
Homework Helper
26,258
618
Your answer to question 1) is correct.

For 2) write 500050=10001*50 and think about it.
 
Last edited:
  • #4
done it :D

107^2 + 699^2

thnx man

is there actually an elegant way of picking the factors outa 500050 or is it simply guesstimation?
 
  • #5
Dick
Science Advisor
Homework Helper
26,258
618
I just picked the obvious factors of 500050. If they had chosen odder ones it would have been much harder as I don't know any really systematic way of finding 'square+1' factors except trial and error.
 

Related Threads on 2 questions please

Replies
8
Views
2K
Top