Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

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)

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