Hey Sy could you maybe give a few hints for this question? I can only get part ii)...
What exactly are you allowed to assume about addition/subtraction in i) and ii)? On which sets is it defined and what does it map pairs of elements from this set into? Just saying that the sum of two positive integers is a positive integer doesn't seem to be enough. (Given that we don't have a rigorous definition of the integers or +,- here.)Just an exercise in mathematical/logical argument and proof:
i) A straightforward induction. The key step:
can you solve the questions in the current advanced thread?Oh I forgot iv).
Well just sub in
to the identity proven in iii).
You can also find a surdic expression for x if you are that way inclined, by using double angle formulae for example.
Oh, I didn't realise there were unanswered ones. I'll try them tomorrow.can you solve the questions in the current advanced thread?
will be waitingOh, I didn't realise there were unanswered ones. I'll try them tomorrow.
Can only do iii atm (my solution could be wrong...):-------------------------------
Extending on the question:
Part ii):
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Extending on the question:
i)Easy mechanics question from an HSC paper before you guys start confusing me again.