Drsoccerball
Well-Known Member
- Joined
- May 28, 2014
- Messages
- 3,647
- Gender
- Undisclosed
- HSC
- 2015
Re: HSC 2015 4U Marathon - Advanced Level
 \\ RHS= x^2 (x^2 +2 +\frac{1}{x^2} +x + \frac{1}{x}+1) \\= x^4 +2x^2 +1 +x^3 +x +x^2 \\ =x^4 +x^3 +3x^2 +x +1 ?... )
Next:
For 2015er's
1. Show that if w = 1/x + x
Then w^2 - 2 =x^2 + 1/x^2
2. Use part 1 to show that x^4+....+x+1 = x^2*(w^2+w+1)
And hence factorise the x^4+x^3+...+x+1
3. Solve x^5=1
4. Hence deduce using all parts above to find an exact value for cos (pi/5)) and cos (2pi/5)
5. Repeat the process this time expressing x and w in mod arg form.