SOLUTION: Find a number such that 1 less than the number divided by the reciprocal of the number is equal to 1. (Leave the answeres in exact form, that is with the square root.)

SOLUTION: Find a number such that 1 less than the number divided by the reciprocal of the number is equal to 1. (Leave the answeres in exact form, that is with the square root.)

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Question 131543: Find a number such that 1 less than the number divided by the reciprocal of the number is equal to 1. (Leave the answeres in exact form, that is with the square root.)
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
let x be the number.
(x-1) / 1/x =1
(x-1) *x=1
x^2-x=1
x^2-x-1=0
x^2-x =1
x^2-x+ 1/4=1+ 1/4
(x- 1/2)^2=5/4
x- 1/2=+-sqrt(5/4)
x=1/2+-sqrt(5)/2
x=(1+sqrt(5))/2, x=(1-sqrt(5))/2
.
Ed
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