dasda
Badges: 12
Rep:
?
#1
Report Thread starter 1 week ago
#1
Need help with this question. Thanks
Attached files
Last edited by dasda; 1 week ago
0
reply
RDKGames
Badges: 20
Rep:
?
#2
Report 1 week ago
#2
(Original post by dasda)
Need help with this question. Thanks
What have you tried? The proof is pretty much the same as for \sqrt{2}.
0
reply
dasda
Badges: 12
Rep:
?
#3
Report Thread starter 1 week ago
#3
(Original post by RDKGames)
What have you tried? The proof is pretty much the same as for \sqrt{2}.
I cubed both sides and ended up with 2=a^3/b^3. I then put 2a^3=b^3. I then said that b=(2n)^3
0
reply
RDKGames
Badges: 20
Rep:
?
#4
Report 1 week ago
#4
(Original post by dasda)
I cubed both sides and ended up with 2=a^3/b^3. I then put 2a^3=b^3. I then said that b=(2n)^3
You are jumping across landscapes here with this argument. Too many missing links to a point where you're confusing yourself.

Firstly, you need to hammer down the fact that you assume cube root 2 is rational, this means expressing it in the irreducible form a/b where a is some integer and b is a natural number. The irreducible part is key here.

Secondly, you cube both sides and get 2 = a^3/b^3 and this is the same as 2b^3 = a^3. You got this the wrong way round in yours. Be careful!
So, we know that a^3 is even. What does this tell us about a itself?
Last edited by RDKGames; 1 week ago
1
reply
dasda
Badges: 12
Rep:
?
#5
Report Thread starter 1 week ago
#5
(Original post by RDKGames)
You are jumping across landscapes here with this argument. Too many missing links to a point where you're confusing yourself.

Firstly, you need to hammer down the fact that you assume cube root 2 is rational, this means expressing it in the form a/b where a and b are irreducible. And that's a key word.

Secondly, you cube both sides and get 2 = a^3/b^3 and this is the same as 2b^3 = a^3. You got this the wrong way round in yours. Be careful!
So, we know that a^3 is even. What does this tell us about a itself?
A is even.
0
reply
RDKGames
Badges: 20
Rep:
?
#6
Report 1 week ago
#6
(Original post by dasda)
A is even.
Therefore you can express it in the form a=2n for some integer n. What next?
0
reply
dasda
Badges: 12
Rep:
?
#7
Report Thread starter 1 week ago
#7
a=2n^3
0
reply
RDKGames
Badges: 20
Rep:
?
#8
Report 1 week ago
#8
(Original post by dasda)
a=2n^3
Nope. Where did that come from?
0
reply
dasda
Badges: 12
Rep:
?
#9
Report Thread starter 1 week ago
#9
(Original post by RDKGames)
Nope. Where did that come from?
i assumed since a was even and the equation has a^3, we would cube 2n
0
reply
RDKGames
Badges: 20
Rep:
?
#10
Report 1 week ago
#10
(Original post by dasda)
i assumed since a was even and the equation has a^3, we would cube 2n
Yes we do, but you cubed it incorrectly, and didn't write a^3 to indicate it. If you're cubing 2n you need to cube the 2 as well.

(2n)^3 = 2^3n^3
0
reply
dasda
Badges: 12
Rep:
?
#11
Report Thread starter 1 week ago
#11
so 8n^3
0
reply
RDKGames
Badges: 20
Rep:
?
#12
Report 1 week ago
#12
(Original post by dasda)
so 8n^3
Yes, a^3 = 8n^3. What next?
0
reply
dasda
Badges: 12
Rep:
?
#13
Report Thread starter 1 week ago
#13
(Original post by RDKGames)
Yes we do, but you cubed it incorrectly, and didn't write a^3 to indicate it. If you're cubing 2n you need to cube the 2 as well.

(2n)^3 = 2^3n^3
is it 8a^3=b^3
0
reply
RDKGames
Badges: 20
Rep:
?
#14
Report 1 week ago
#14
(Original post by dasda)
is it 8a^3=b^3
Nope.

We have 2b^3 = a^3 so it becomes 2b^3 = 8n^3.
0
reply
dasda
Badges: 12
Rep:
?
#15
Report Thread starter 1 week ago
#15
(Original post by RDKGames)
Nope.

We have 2b^3 = a^3 so it becomes 2b^3 = 8n^3.
this is the step I am unsure about. I would divide both sides by 2
0
reply
RDKGames
Badges: 20
Rep:
?
#16
Report 1 week ago
#16
(Original post by dasda)
this is the step I am unsure about. I would divide both sides by 2
Yep, so b^3 = 4n^3. What does this tell you about about b^3 ?? Hence b ?
0
reply
dasda
Badges: 12
Rep:
?
#17
Report Thread starter 1 week ago
#17
I would say b is even.
0
reply
RDKGames
Badges: 20
Rep:
?
#18
Report 1 week ago
#18
(Original post by dasda)
I would say b is even.
Indeed. Do you see the contradiction now? Since a and b must both be even.

Have a look at my post #4 on this thread and what assumptions we have made if you're not seeing the contradiction immediately.
0
reply
dasda
Badges: 12
Rep:
?
#19
Report Thread starter 1 week ago
#19
(Original post by RDKGames)
Indeed. Do you see the contradiction now? Since a and b must both be even.

Have a look at my post #4 on this thread and what assumptions we have made if you're not seeing the contradiction immediately.
you assumed that the irrational was irreducible. but we got a factor of 2 and 1 so our assumption is incorrect
0
reply
dasda
Badges: 12
Rep:
?
#20
Report Thread starter 1 week ago
#20
is that a correct line of thinking

(Original post by RDKGames)
Indeed. Do you see the contradiction now? Since a and b must both be even.

Have a look at my post #4 on this thread and what assumptions we have made if you're not seeing the contradiction immediately.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top

University open days

  • University of Stirling
    Undergraduate Open Day Undergraduate
    Thu, 26 Sep '19
  • Heriot-Watt University
    Undergraduate Open Day - Scottish Borders Campus Undergraduate
    Fri, 27 Sep '19
  • Royal Holloway, University of London
    Undergraduate open day Undergraduate
    Sat, 28 Sep '19

Are you attending a Global Climate Strike?

Yes, I'm striking (19)
7.09%
No, but I wanted to/I support the cause (152)
56.72%
No (97)
36.19%

Watched Threads

View All