Is x = -1 a Valid Solution for the Equation x/1 = x + 1/x?

[hedons]

x/1 = x+1/x

 

[RandallB]

0/0 . . or
SqrRoot of -0

 

[K.J.Healey]

My answer is "hedons"

 

[nnnnnnnn]

x/1 = x
so your eq becomes:

x = x - 1/x
->0=-1/x...
unless you take the limit you are nobody...

 

[hemmul]

x/1 = x+1/x

x=±sqrt(1/(1-1))

you're the 4 grade student, who just studied what an "equation" is

 

[theCandyman]

x/1 = x+1/x

Is that written as $$\frac {x}{1} = x + \frac{1}{x}$$ or is it supposed to be $$\frac {x}{1} = \frac{x+1}{x}$$?

 

[K.J.Healey]

oh yea, cause if its the second one then its the golden ratio. 1.61828 or whatever.

 

[ArielGenesis]

Is that written as $$\frac {x}{1} = x + \frac{1}{x}$$ or is it supposed to be $$\frac {x}{1} = \frac{x+1}{x}$$?

then if it's the second

x^2 = x+1
x^2-x-1 =0
x=(1(+-) (((-1)^2)-(4)(1)(-1))^0.5) (2(1))^-1
x= (1(+-)(5^0.5))/2
interesting ?

 

[SolidFist]

An anomoly, that's what you are!

 

[vikasj007]

i think it should be infinity. putting value of xas infinite we will satisfy the equation.

 

[xJuggleboy]

Are we ever getting a answer here?

 

[pack_rat2]

x = 1/x has no solution. For x = 1 + 1/x, x = ~1.618 (the "golden ratio").

 

[bjr_jyd15]

x = 1/x has no solution.

?! I think x=1 is a solution.

 

[theCandyman]

So is $$x = -1$$.

 

[hypermorphism]

?! I think x=1 is a solution.

I believe he meant to say 0=1/x.

 

[pack_rat2]

So is $$x = -1$$.

Ahhhh...x = 1 is so obvious. but x = -1 doesn't work.