A lvl H2 Maths: Inequalities

Question from http://www.sgforums.com/forums/2297/topics/343748

Find the set of values of x for which (e^x2) / (x-1) - 8x > 0.
Hence, solve (e^x2) / ( |x| - 1) - |8x| > 0.

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Answer:

Plot

(i) y = (e^x2) / (x-1)
(ii) y = 8x



For (e^x2) / (x-1) > 8x,
-1.9587 <> 0.9999




(e^x2) / ( |x| - 1) - |8x| > 0
(e^|x|2) / ( |x| - 1) - 8|x| > 0
Sub x = |x|
-1.9587 < |x| < -0.1138 (reject) , |x| > 0.9999

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