Question

51.

If x2 - x + 1 = 0 then find the value of x18 + x15 + x12 +x9 +x6 + x3 + 18

Answer 1

Given that
$x = \frac{1 + \sqrt{ - 3} }{2}$
Convert this to polar form.
$x = \cos(60) + \sqrt{ - 1} \sin(60)$
Then use De Moivre's Theorem to get
${x}^{18} = \cos(60 \times 18) + { \sqrt{ - 1} }^{18} \sin(60 \times 18) \\ {x}^{18} = \cos(0) - \sin(0) \\ {x}^{18} = 1 - 0 = 1$
Then use this again and again to get the values for the rest of the polynomials and then substitute to find the answer.
Good Luck!!

Answer 2

Answer:

Step-by-step explanation: