SOLUTION: When the reciprocal of the number is subtracted from the number itself, the result equals one more than the reciprocal of the number. Find the number(s).
I have the equation se
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I have the equation se
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Question 918746: When the reciprocal of the number is subtracted from the number itself, the result equals one more than the reciprocal of the number. Find the number(s).
I have the equation set up as: x - 1/x = 1 + 1/x Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! you got it right.
x - 1/x = 1 + 1/x
subtract 1/x from both sides of the equation to get:
x - 2/x = 1
multiply both sides of the equation by x to get:
x^2 - 2 = x
subtract x from both side of the equation to get:
x^2 - x - 2 = 0
factor to get:
(x-2) * (x+1) = 0
solve for x to get:
x = 2 or x = -1
when x = 2:
x - 1/x = 1 + 1/x becomes:
2 - 1/2 = 1 + 1/2 which becomes:
1 and 1/2 = 1 and 1/2 which is true.
when x = -1:
x - 1/x = 1 + 1/x becomes:
-1 - (-1/1) = 1 + (-1/1 which becomes:
-1 + 1 = 1 - 1 which becomes
0 = 0 which is true.
