SOLUTION: what positive number is the same as its reciprocal?

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Question 773866: what positive number is the same as its reciprocal?
Answer by jim_thompson5910(35256) About Me  (Show Source):
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a/b = b/a

a*a = b*b

a^2 = b^2

a^2 - b^2 = 0

(a - b)(a+b) = 0

a-b=0 or a+b = 0

a = b or a = -b

if a = b, then a/b = b/a turns into 1 = 1. Similarly, if a = -b, then we get -1 = -1

So the number 1 is the only positive number that has an equal reciprocal.