In order to find values of expressions involving a, b, c when these quantities are connected by the equation , we might employ the substitution:
If, however, the expressions involve a, b, c symmetrically the method exhibited by the following example is preferable:
Example:
If , show that
Solution:
We have identically
, where
,
,
.
Hence, using the condition given,
Taking logarithms and equating the coefficients of , we have
, which is equal to the coefficient of
in the expansion of
, which is equal to the coefficient of
in the following:
By putting we obtain
, and hence, we get
, and the required result follows at once.
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Nalin Pithwa