Elementary-algebra-If-x-1-17-2-Find-the-value-of-E-x-8-x-7-x-6-x-1-x-6-x-3-1-

Question Number 190883 by mnjuly1970 last updated on 13/Apr/23

Elementary algebra

If, x = \frac{1 + \sqrt{17}}{2} \Rightarrow Find the value of :

E = \frac{x^{8} - x^{7} + x^{6} - \dots . - x + 1}{x^{6} - x^{3} + 1} = ?

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Answered by Frix last updated on 13/Apr/23

E = \frac{(x^{2} - x + 1) (x^{6} - x^{3} + 1)}{x^{6} - x^{3} + 1} = x^{2} - x + 1 = 5

Answered by mnjuly1970 last updated on 13/Apr/23

E = \frac{\frac{1 + x^{9}}{1 + x}}{1 - x^{3} + x^{6}} = \frac{1 + x^{9}}{(1 + x) (1 - x^{3} + x^{6})}

= \frac{1 + x^{3}}{1 + x} = 1 - x + x^{2}

= 1 - x (1 - x)

= 1 - (\frac{1 + \sqrt{17}}{2}) (\frac{1 - \sqrt{17}}{2})

= 1 - \frac{- 16}{4} = 5 ✓