If a,b,c are three distinct nonzero real numbers and
for some real number t
prove that .
so we have: which we will call 1), 2), and 3) respectively.
now first subtract 2) from 1), then 3) from 2), and finally 1) from 3) to get:
and multiply the equations together:
which, since gives us:
this time multilpy 1) by , 2) by , and 3) by to get:
which we'll call 4), 5), and 6) respectively. now subtract 5) from 4), then 6) from 5) and finally 4) from 6)
to get: and multiply the equations together:
which, since gives us:
now by and thus: since so: and hence by