## Miscellaneous Example of Algebra

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.

More stuff to follow…

*Nalin Pithwa*

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