**Question**

**Introduction**

This
question was posted to a Facebook forum for Secondary School and Junior College
mathematics (the equivalent of grade 7 and above). Most students, except a few enthusiastic ones
or maybe some from “integrated programme” schools, will not bother with differentiation
from first principles. However, mathematical formulas are true because mathematicians
took the trouble to critically analyse them and show that they always work, not
because they are found in the textbook, nor because the teacher says so.

**Solution**

**Remarks**

The answer to
the original problem just falls out by letting

*p*= 17 and*q*= 19.
Some people
suggested using Binomial Expansion for rational powers. I feel that this is not from first principles,
since Binomial Expansion relies on differentiation, which relies on first
principles.

**Suitable Levels**

*****GCE ‘O’ Level Additional Mathematics

* college level calculus

*****AP Calculus

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