SOLUTION: Quotient of two and a number is the sum of the number and its reciprocal

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Question 1046315: Quotient of two and a number is the sum of the number and its reciprocal
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let's number be x
Quotient of two and a number is:2%2Fx
it is equal to the sum of the number x and its reciprocal 1%2Fx:
2%2Fx=x%2B1%2Fx
2%2Fx-x-1%2Fx=0
%282%2Fx-1%2Fx%29-x=0
1%2Fx-x=0........both sides multiply by x
%281%2Fx%29x-x%2Ax=0%2Ax
%281%2Fcross%28x%29%29cross%28x%29-x%5E2=0
1-x%5E2=0...factor
%281-x%29%281%2Bx%29=0
solutions:
if %281-x%29=0->x=1
if %281%2Bx%29=0->x=-1

so, your number could be 1 or -1