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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 22:38:24)
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