Find-the-range-of-value-of-x-given-that-x-i-1-x-

Question Number 51721 by Tawa1 last updated on 29/Dec/18

Find the range of value of x given that : ∣ x + i ∣ ⩾ \frac{1}{x}

Answered by ajfour last updated on 29/Dec/18

\sqrt{1 + x^{2}} ⩾ \frac{1}{x}

x < 0 a n d i f x > 0 t h e n

l e t x^{2} = y

\Rightarrow y (1 + y) ⩾ 1

\Rightarrow y^{2} + y - 1 ⩾ 0

{(y + \frac{1}{2})}^{2} ⩾ \frac{5}{4}

\Rightarrow y ⩾ \frac{\sqrt{5} - 1}{2}

o r x ⩾ \sqrt{\frac{\sqrt{5} - 1}{2}}

s o x \in (- \infty, 0) \cup [\sqrt{\frac{\sqrt{5} - 1}{2}}, \infty) .

Commented by Tawa1 last updated on 30/Dec/18

God bless you sir

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