A F.5 student, Yan, asked me to do the following without using calculator
As I guessed, he was playing with cubic equations. The first idea came to my mind was, if we CAN evaluate that stuff by bare hands, the numbers should be perfect cube. Then I tried
How lucky I was! Then I gave the solution as follows
In the old syllabus of additional mathematics, students were required to know how to evaluate the following
Nothing special indeed.
Just for further discussion, if the value of gets near to zero,
– – – – – – (*)
Umm, the approximation is not bad, right?
How to get the approximation like (*), believe me, it is extremely easy to create something like that by applying binomial theorem (discussed in applied mathematics (II) or mathematics and statistics).
[OT] Here’s a question for F.2 or F.5 boys. See which form will obtain the correct answer first?