SOLUTION: Determine those real numbers a for which the opposite of a is the same as the reciprocal of a. Since a can be any number, wouldnt a- be the only real number? I'm confused. Ple

Question 256067: Determine those real numbers a for which the opposite of a is the same as the reciprocal of a.
Since a can be any number, wouldnt a- be the only real number? I'm confused. Please help.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

be any real number. Then the opposite of

and the reciprocal of

. We are interested in the value of

when the opposite is equal to the reciprocal, so:

Multiply both sides by

Multiply both sides by -1:

Which has no real number solutions. Hence, the set of all real numbers such that the opposite is equal to the reciprocal is the empty set. Symbolically:

John

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