Where should the values be placed to correctly solve for x?

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Discussion Overview

The discussion revolves around solving the equation x = 2 + 1/x, focusing on the correct placement of values and methods for solving the resulting quadratic equation. Participants explore various approaches to manipulate the equation and derive solutions.

Discussion Character

  • Mathematical reasoning, Homework-related, Technical explanation

Main Points Raised

  • One participant initially presents the equation x = 2 + 1/x and claims to derive x = 4, but does not provide a clear method for this conclusion.
  • Another participant suggests multiplying both sides by x to form a quadratic equation, indicating this as a potential method for solving for x.
  • A subsequent reply proposes the quadratic equation x^2 - 2x - 1 = 0, expressing uncertainty about its solvability and arriving at an approximate value of 2.41 for x.
  • Another participant confirms the quadratic equation and provides the solutions x = 1 ± sqrt(2), but does not clarify how they arrived at this conclusion.
  • A later post details the calculation of the discriminant and the solutions derived from the quadratic formula, presenting the solutions in both radical and simplified forms.
  • One participant expresses gratitude for the clarification provided in the last post, indicating it helped them understand the placement of values better.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct solution to the equation, with multiple approaches and interpretations presented. Some express uncertainty about the solvability of the quadratic equation.

Contextual Notes

There are unresolved aspects regarding the initial claims and the methods used to derive solutions, particularly concerning the accuracy of the values and the steps taken to arrive at them.

06Rousher
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"x=2+1/x"

What I got is this: -x^2=2 then x^2=-2, then x=4
 
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Re: Wanting to make I got this correct

x = 2 + 1/x

To find x, I think it would be appropriate to multiply both sides with x, and solve the quadratic equation.
 
Last edited:
Re: Wanting to make I got this correct

lfdahl said:
x = 2 + 1/x

To find x, I think it would be appropriate to multiply both sides with x, and solve the quadratic equation

So x^2-2x-1? Doesn't seem like that would be solvable.

I got 2.41 for x
 
Re: Wanting to make I got this correct

Why not? You did solve the equation:

x^2-2x-1 = 0 --> x = 1+/- sqrt(2)
 
Re: Wanting to make I got this correct

lfdahl said:
Why not? You did solve the equation:

x^2-2x-1 = 0 --> x = 1+/- sqrt(2)

How did you get to x=1 +/- sqrt(2)?
 
Re: Wanting to make I got this correct

The quadratic equation: x2- 2x - 1 = 0

Discriminant: D = (-2)2-4(1)(-1) = 8

The two solutions:

x1 = (2 + sqrt(8))/2 and x2 = (2 - sqrt(8))/2

or

x1 = 1 + sqrt(2) and x2 = 1 - sqrt(2)

In general for solving a quadratic equation:

\[ax^{2}+bx+c=0 \\\\D = b^{2}-4ac \\\\x = \frac{-b\pm \sqrt{D}}{2a}\]
 
Last edited:
Re: Wanting to make I got this correct

Thank you so much

That last part really helped me understand it, I was having trouble on where to place the values
 

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