x-2-x-lt-2-x-find-solution-set-

Question Number 100660 by bobhans last updated on 28/Jun/20

∣ x^{2} - x ∣ < 2 + x . f i n d s o l u t i o n s e t .

Commented by bramlex last updated on 28/Jun/20

s i n c e ∣ x^{2} - x ∣ ⩾ 0 t h e n 2 + x m u s t b e > 0

(1) 2 + x > 0; x > - 2

(2) (x^{2} - x - x - 2) (x^{2} - x + x + 2) < 0

(x^{2} - 2 x - 2) (x^{2} + 2) < 0

{(x - 1)}^{2} - {(\sqrt{3})}^{2} < 0

(x - 1 - \sqrt{3}) (x - 1 + \sqrt{3}) < 0

1 - \sqrt{3} < x < 1 + \sqrt{3}

s o l u t i o n s e t w e g e t f r o m (1) \cap (2)

∴ 1 - \sqrt{3} < x < 1 + \sqrt{3}

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