SOLUTION: The sum of a positive real number and six times its reciprocal is equal to its cube. What is the square of the number?

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Question 808593: The sum of a positive real number and six times its reciprocal is equal to its cube. What is the square of the number?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the number be x
x + (6/x) = x^3
(x^2+6)/x=x^3
x^2+6=x^4
x^4-x^2-6=0
x^4-3x^2+2x^2-6=0
x^2(x-3)+2x(x-3)=0
(x^2-3)(x^2+2x)=0
x(x^2-3)(x+2)=0
x=0, x= +/- sqrt(3) x=-2
You can find the squares