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Prove by contradiction
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Last edited by dasda; 1 year ago
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#2
(Original post by dasda)
Need help with this question. Thanks
Need help with this question. Thanks
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#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
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
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 year ago
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(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?
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?
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#6
(Original post by dasda)
A is even.
A is even.
for some integer 
. What next?
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(Original post by RDKGames)
Nope. Where did that come from?
Nope. Where did that come from?
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#10
(Original post by dasda)
i assumed since a was even and the equation has a^3, we would cube 2n
i assumed since a was even and the equation has a^3, we would cube 2n
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(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.
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.
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#16
(Original post by dasda)
this is the step I am unsure about. I would divide both sides by 2
this is the step I am unsure about. I would divide both sides by 2
. What does this tell you about about 
?? Hence 
?
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#18
(Original post by dasda)
I would say b is even.
I would say b is 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.
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(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.
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.
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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.
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.
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