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Proof by contradiction

Is anybody able to help me answer this, I'm completely stuck!
Thanks!
Prove by contradiction that there are no positive integers a and b, with a odd, such that

a + 2b = Root8ab .
Reply 1
Original post by wills21
Is anybody able to help me answer this, I'm completely stuck!
Thanks!
Prove by contradiction that there are no positive integers a and b, with a odd, such that

a + 2b = Root8ab .


Is that
sqrt(8ab)
or
sqrt(8)ab
(edited 4 years ago)
Original post by wills21
Is anybody able to help me answer this, I'm completely stuck!
Thanks!
Prove by contradiction that there are no positive integers a and b, with a odd, such that

a + 2b = Root8ab .


Suppose there there is a pair of integers (a,b), with a odd, such that

a+2b=8aba + 2b = \sqrt{8ab}

Then (a+2b)2=8ab(a+2b)^2 = 8ab

Note that a+2b is (odd)+(even) hence it is (odd) and so the square (a+2b)^2 is odd ... but what's the problem ??
Reply 3
Original post by mqb2766
Is that
sqrt(8ab)
or
sqrt(8)ab

(8ab)
Reply 4
Original post by RDKGames
Suppose there there is a pair of integers (a,b), with a odd, such that

a+2b=8aba + 2b = \sqrt{8ab}

Then (a+2b)2=8ab(a+2b)^2 = 8ab

Note that a+2b is (odd)+(even) hence it is (odd) and so the square (a+2b)^2 is odd ... but what's the problem ??

that’s the question. simply “prove my contradiction” and it’s 4 marks (edexcel alevel maths)
Reply 5
Original post by wills21
that’s the question. simply “prove my contradiction” and it’s 4 marks (edexcel alevel maths)

Yes they've given you a big hint, they're asking you what the problem is (i.e. can you spot the contradiction now?)
Ahh just spotted it
Reply 7
Original post by wills21
Is anybody able to help me answer this, I'm completely stuck!
Thanks!
Prove by contradiction that there are no positive integers a and b, with a odd, such that

a + 2b = Root8ab .

where can i find this question paper? thanks
Reply 8
Original post by llleahll
where can i find this question paper? thanks

is it aqa or edexcel?
anyone know what paper this question is from?
I think it is the Edexcel 2020 mock paper set 2 but only teachers can access it.
any answer to this?
Reply 12
Original post by Hasan167
any answer to this?

Do you mean the original question? That was answered a year ago in post #3 :smile:
Bb
Look at all the people here trying to cheat, loooooollllll
Original post by RDKGames
Suppose there there is a pair of integers (a,b), with a odd, such that

a+2b=8aba + 2b = \sqrt{8ab}

Then (a+2b)2=8ab(a+2b)^2 = 8ab

Note that a+2b is (odd)+(even) hence it is (odd) and so the square (a+2b)^2 is odd ... but what's the problem ??

But the question doesn’t clarify whether b is odd or even, and if b is also odd then surely the equation can work?
Original post by olliebrown6
But the question doesn’t clarify whether b is odd or even, and if b is also odd then surely the equation can work?

Trying out a few numbers may be useful?
Original post by olliebrown6
But the question doesn’t clarify whether b is odd or even, and if b is also odd then surely the equation can work?

Yes but it doesnt matter what b is, as it is 2b it is a multiple of 2 and a multiple of two always even e.g if b is 3 2b is 6 which is even etc :smile:
Original post by wills21
Is anybody able to help me answer this, I'm completely stuck!
Thanks!
Prove by contradiction that there are no positive integers a and b, with a odd, such that

a + 2b = Root8ab .


By any chance do you remember what question paper this is from
Original post by wills21
that’s the question. simply “prove my contradiction” and it’s 4 marks (edexcel alevel maths)

Do you know the specific paper??

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