# Prove by contradiction

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Need help with this question. Thanks

Last edited by dasda; 1 year ago

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#2

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Need help with this question. Thanks

**dasda**)Need help with this question. Thanks

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#4

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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

**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

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

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

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?

**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?

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#6

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A is even.

**dasda**)A is even.

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(Original post by

Nope. Where did that come from?

**RDKGames**)Nope. Where did that come from?

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#10

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i assumed since a was even and the equation has a^3, we would cube 2n

**dasda**)i assumed since a was even and the equation has a^3, we would cube 2n

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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.

**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.

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#16

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this is the step I am unsure about. I would divide both sides by 2

**dasda**)this is the step I am unsure about. I would divide both sides by 2

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#18

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I would say b is even.

**dasda**)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

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.

**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.

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is that a correct line of thinking

(Original post by

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.

**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.

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