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#1 2012-11-05 01:07:11

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,862
Website

Those inequalities again

Prove that in a quadrilateral ABCD,
AB + BC + CD > DA


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#2 2012-11-05 01:14:37

bob bundy
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Registered: 2010-06-20
Posts: 6,531

Re: Those inequalities again

hi

Split your quadrilateral into two triangles and use the triangle inequality twice.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2012-11-05 01:25:36

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,862
Website

Re: Those inequalities again

Tried...But how do I get rid of the diagonal in the equation?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#4 2012-11-05 01:39:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Those inequalities again

You can do it like this:

CD<AC+AD<(AB+BC)+AD. Q.E.D

Last edited by anonimnystefy (2012-11-05 01:40:45)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2012-11-05 02:40:53

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,862
Website

Re: Those inequalities again

Yes! smile Thanks to bob bundy and anonimnystefy


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#6 2012-11-05 02:43:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Those inequalities again

You are welcome!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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