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#1 2008-07-06 00:37:47

tony123
Member
Registered: 2007-08-03
Posts: 189

three distinct

If a,b,c are three distinct nonzero real numbers and

for some real number t

prove that

.

Last edited by tony123 (2008-07-06 00:38:24)

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#2 2009-03-22 04:55:39

Kurre
Member
Registered: 2006-07-18
Posts: 280

Re: three distinct




Now we multiply (1) by b, (2) by c and subtract, and also we subtract (3) multiplied by a from (1) multiplied by b, yielding:


Now we also multiply (2) by ac, (1) by c b and subtract, yielding:

inserting (a-c) in (4) from (6) yields:

and multiplying this by a/t (t nonzero) and using (5)


since the numbers where distinct,
, thus

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