Solve-the-inequality-9-x-1-4-x-18-0-

Question Number 22244 by ajfour last updated on 14/Oct/17

S o l v e t h e i n e q u a l i t y :

- 9 (\sqrt[4]{x}) + \sqrt{x} + 18 ⩾ 0 .

Answered by $@ty@m last updated on 14/Oct/17

L e t \sqrt{x} = y

- 9 \sqrt{y} + y + 18 ⩾ 0

9 \sqrt{y} ⩽ 18 + y

81 y ⩽ 324 + y^{2} + 36 y

y^{2} - 45 y + 324 ⩾ 0

(y - 9) (y - 36) ⩾ 0

y \in (- \infty, 9] \cup [36, \infty)

x \in (0, 81] \cup [1296, \infty)

Commented by ajfour last updated on 14/Oct/17

T h a n k s, t h i s m a t c h e s w i t h t h e

a n s w e r g i v e n .

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