Back
to top
Help with question
Watch this threadPage 1 of 1
Go to first unread
Skip to page:
Cpt Avocado
Badges:
9
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1
An integer N is the sum of the squares of two different integers.
i) Prove that N^2 is also the sum of the squares of two integers.
So far I have tried:
N = a^2 + b^2
N^2 = (a^2 + b^2)^2 = a^4 + b^4 + a^2b^2
i) Prove that N^2 is also the sum of the squares of two integers.
So far I have tried:
N = a^2 + b^2
N^2 = (a^2 + b^2)^2 = a^4 + b^4 + a^2b^2
0
reply
Pangol
Badges:
15
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2
Report
#2
(Original post by Cpt Avocado)
An integer N is the sum of the squares of two different integers.
i) Prove that N^2 is also the sum of the squares of two integers.
So far I have tried:
N = a^2 + b^2
N^2 = (a^2 + b^2)^2 = a^4 + b^4 + a^2b^2
An integer N is the sum of the squares of two different integers.
i) Prove that N^2 is also the sum of the squares of two integers.
So far I have tried:
N = a^2 + b^2
N^2 = (a^2 + b^2)^2 = a^4 + b^4 + a^2b^2
I'm sure you'll agree that 2a^2b^2 = 4a^2b^2 - 2a^2b^2. Can you see how this helps you?
0
reply
RDKGames
Badges:
20
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3
Report
#3
(Original post by Cpt Avocado)
An integer N is the sum of the squares of two different integers.
i) Prove that N^2 is also the sum of the squares of two integers.
So far I have tried:
N = a^2 + b^2
N^2 = (a^2 + b^2)^2 = a^4 + b^4 + a^2b^2
An integer N is the sum of the squares of two different integers.
i) Prove that N^2 is also the sum of the squares of two integers.
So far I have tried:
N = a^2 + b^2
N^2 = (a^2 + b^2)^2 = a^4 + b^4 + a^2b^2
N^2 = a^4 + b^4 + 2a^2b^2
Anyway, rewrite as
(a^4 - 2a^2b^2 + b^4) + 4a^2b^2
and finish off from there.
0
reply
Cpt Avocado
Badges:
9
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#4
(Original post by Pangol)
You should have two lots of a^2b^2, not just one.
I'm sure you'll agree that 2a^2b^2 = 4a^2b^2 - 2a^2b^2. Can you see how this helps you?
You should have two lots of a^2b^2, not just one.
I'm sure you'll agree that 2a^2b^2 = 4a^2b^2 - 2a^2b^2. Can you see how this helps you?
0
reply
Cpt Avocado
Badges:
9
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#5
So it's (a^2 - b^2)^2 + (2ab)^2
My brain just doesn't make that leap
Thanks tho!
My brain just doesn't make that leap
Thanks tho!
0
reply
Pangol
Badges:
15
Rep:
?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#6
Report
#6
(Original post by Cpt Avocado)
So it's (a^2 - b^2)^2 + (2ab)^2
My brain just doesn't make that leap
Thanks tho!
So it's (a^2 - b^2)^2 + (2ab)^2
My brain just doesn't make that leap
Thanks tho!
1
reply
X
Page 1 of 1
Go to first unread
Skip to page:
Quick Reply
