solve-1-x-x-2-2-x-x-2-

Question Number 180785 by Vynho last updated on 17/Nov/22

s o l v e (1 - x - x^{2} \dots) (2 - x - x^{2} \dots)

Answered by Rasheed.Sindhi last updated on 17/Nov/22

(1 - (x + x^{2} + \dots)) (2 - (x + x^{2} + \dots))

I f ∣ x ∣< 1 :

(1 - \frac{x}{1 - x}) (2 - \frac{x}{1 - x})

\frac{1 - x - x}{1 - x} \cdot \frac{2 - 2 x - x}{1 - x}

= \frac{(1 - 2 x) (2 - 3 x)}{{(1 - x)}^{2}} = \frac{6 x^{2} - 7 x + 2}{x^{2} - 2 x + 1}

Answered by mr W last updated on 17/Nov/22

l e t t = x + x^{2} + \dots = x (1 + x + x^{2} + \dots)

\Rightarrow (1 - t) (2 - t) = 0

\Rightarrow t = 1 o r 2

\Rightarrow x (1 + x + x^{2} + \dots) = 1 o r 2

x < 1

\frac{x}{1 - x} = 1 o r 2

\Rightarrow x = \frac{1}{2} o r \frac{2}{3}

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