Answer only one of the following two alternatives. **EITHER** Let `ω = cos(π/5) + i sin(π/5)`. Show that `ω⁵ + 1 = 0` and deduce that `ω⁴ – ω³ + ω² – ω = -1`. [2] Show further that `ω - ω⁴ = 2 cos(π/5)` and `ω³ - ω² = 2 cos(2π/5)`. [4] Hence find the values of `cos(π/5) + cos(2π/5)` and `cos(π/5) cos(2π/5)`. [4] Find a quadratic equation having roots `cos(π/5)` and `cos(2π/5)` and deduce the exact value of `cos(π/5)`. [4] **OR** Given that `x² d²y/dx² + 4x(1+x) dy/dx + 2(1 + 4x + 2x²)y = 8x²` and that `x²y = z`, show that `d²z/dx² + 4 dz/dx + 4z = 8x²`. [4] Find the general solution for y in terms of x. [8] Describe the behaviour of y as x → ∞. [2]