Mathematical Proof

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beachpanda
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#1
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#1
Is anyone able to help me prove the following is true? Where x & y are positive non-zero values

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I tried writing a fraction with x+y on the top and proving that it's greater than 1, but to no success. Even tried rationalising the denominator but also no luck:

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Thankyou
Last edited by beachpanda; 5 months ago
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ghostwalker
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#2
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#2
(Original post by beachpanda)
Is anyone able to help me prove the following is true? Where x & y are positive non-zero values

Name:  Bildschirmfoto 2021-12-06 um 13.07.04.png
Views: 13
Size:  16.1 KB

I tried writing a fraction with x+y on the top and proving that it's greater than 1, but to no success. Even tried rationalising the denominator but also no luck:

Name:  Bildschirmfoto 2021-12-06 um 13.06.01.png
Views: 4
Size:  5.9 KB
Thankyou
You might like to try looking for a counter-example.
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the bear
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(Original post by beachpanda)
Is anyone able to help me prove the following is true? Where x & y are positive non-zero values

Name:  Bildschirmfoto 2021-12-06 um 13.07.04.png
Views: 13
Size:  16.1 KB

I tried writing a fraction with x+y on the top and proving that it's greater than 1, but to no success. Even tried rationalising the denominator but also no luck:

Name:  Bildschirmfoto 2021-12-06 um 13.06.01.png
Views: 4
Size:  5.9 KB
Thankyou
if you let x and y both equal 1 see what happens
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beachpanda
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(Original post by the bear)
if you let x and y both equal 1 see what happens
I get 4<2 which isn't correct? But I've been told that x+y is greater than the other expression? (It formed part of a much longer question)

(Original post by ghostwalker)
You might like to try looking for a counter-example.
Do you know what sort of counter example? I could switch the inequality sign, or flip the fraction but I come into the same issues.
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the bear
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(Original post by beachpanda)
I get 4<2 which isn't correct? But I've been told that x+y is greater than the other expression? (It formed part of a much longer question)


Do you know what sort of counter example? I could switch the inequality sign, or flip the fraction but I come into the same issues.
the reason you cannot prove the statement is true is that it is false. unless there is some extra information about the value of x and y etc.
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ghostwalker
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(Original post by beachpanda)
I get 4<2 which isn't correct? But I've been told that x+y is greater than the other expression? (It formed part of a much longer question)


Do you know what sort of counter example? I could switch the inequality sign, or flip the fraction but I come into the same issues.
Hopefully you've resolved this issue now.

As to a counter example, it's just a case of plugging some values in which make the assertion false, which is what you have done with the bear's suggestion. That's the counter-example disproving the assertion.
Last edited by ghostwalker; 5 months ago
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