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

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,754
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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'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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

bob bundy
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Registered: 2010-06-20
Posts: 7,064

Re: Those inequalities again

hi

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

Bob


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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,754
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'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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

anonimnystefy
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From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

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
The knowledge of some things as a function of age is a delta function.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,754
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'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

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
The knowledge of some things as a function of age is a delta function.

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