Inequalities

Exercise 4:

Find all solutions of the inequality

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Solution.

This is a preview of coming attractions. There are no rules to apply here; in particular, DO NOT try to divide by x. Why not?

Instead, look at the inequality again: A square of a number is always positive (or zero). Thus, it will never be less than or equal to -1.

By "close inspection", we have found out that the inequality has no solutions; the set of solutions is empty.

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Helmut Knaust
Fri Jul 11 14:32:40 MDT 1997

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