SOLUTION: if the reciprocal of a certain positive number is one less than twice that number, find the number

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Question 167166: if the reciprocal of a certain positive number is one less than twice that number, find the number
Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
the reciprical of x is 1/x.
the reciprical of a/b is b/a
.
let x represent the "certain positive number"
Therefore, the reciprical of x is 1/x and 1/x is one less than twice x so:
1%2Fx=2x-1
.
Solve for x
multiply both sides by x (remember to put parenthesis around the right side so you do not make an error in multiplying).
1%2Fx%2Ax=x%282x-1%29
reduce on the left and distribute on the right side
1=2x%5E2-x
move all terms to the same side
2x%5E2-x-1=0
.
From here you can either plug this into the Quadratic equation or you can complete the square.
.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
x+=+%28-%28-1%29+%2B-+sqrt%28+%281%29%5E2-4%2A%282%29%2A%28-1%29+%29%29%2F%282%2A%282%29%29+
.
x+=+%281+%2B-+sqrt%28+1%2B8+%29%29%2F4+
.
x=%281%2B-3%29%2F4
.
x=1 and x=-1%2F2
.
I hope this helps!
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