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
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Since a can be any number, wouldnt a- be the only real number? I'm confused. Ple
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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):
Let be any real number. Then the opposite of is and the reciprocal of is . 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:
