SOLUTION: My problem is: Determine those real numbers a for which the opposite of a is the same as the reciprocal of a. I am wondering if a*1/a=1/a*a=1 would be an appropriate answer or

Algebra ->  Algebra  -> Inverses -> SOLUTION: My problem is: Determine those real numbers a for which the opposite of a is the same as the reciprocal of a. I am wondering if a*1/a=1/a*a=1 would be an appropriate answer or       Log On

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Question 323071: My problem is: Determine those real numbers a for which the opposite of a is the same as the reciprocal of a.
I am wondering if a*1/a=1/a*a=1 would be an appropriate answer or not.
Answer by rapaljer(4667) About Me  (Show Source):
You can put this solution on YOUR website!
The opposite of a would be -a.

The reciprocal of a would be 1/a.

The question says to find all values of a such that
-a=1/a

Multiply both sides by a:
-a*a=(1/a)*a
-a^2 =1

Add a^2 to each side:
0=a^2+1

Or, rewrite this as a^2=-1.

There are NO REAL VALUES of a for which a^2=-1. NO SOLUTION!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus