ADVANCED EXERCISES-Inequalities


(1) Solve each inequality.

 (a) (x + 5)2(x + 3)(x - 1)  0

 (b) x(1 - x2)3  7(1 - x2)3

 (c) 4x4 - 25x2 + 36  0

 (d) 1     1       2
     - + -----  ------
     x   x + 1    x + 2

 (e)
HINT: Try to apply the techniques of the introductory and moderate sections to these questions. For example, (a) is similar to introductory exercise 2(a), only with more factors. Question (b) could be similar to (a), once 0 has been obtained on one side of the inequality, and then the expression factored.

In question (e), note that is a positive quantity, so the direction of the inequality won't change if it is multiplied by square root of x. Note also that x must be positive here.


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