Using the Quadratic Formula to Solve y + 1/y = x

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Homework Help Overview

The discussion revolves around the equation y + 1/y = x, with participants exploring how to apply the quadratic formula to solve for y. The subject area involves algebraic manipulation and the properties of quadratic equations.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss converting the original equation into a standard quadratic form, questioning how to achieve this through multiplication. There is also a focus on the meaning of "solution" in this context, with some participants clarifying the goal of expressing y as a function of x.

Discussion Status

The discussion is active, with participants providing hints and guidance on how to manipulate the equation. Multiple interpretations of the problem are being explored, particularly regarding the definition of "solution" and the intended outcome of the problem.

Contextual Notes

There is an emphasis on ensuring y is not equal to zero, which may influence the approach to solving the equation. Participants are also considering the implications of the equation's structure on finding a solution.

paridiso
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1. y + 1/y = x
x = (1/2)\sqrt{x^2 - 4} + 1/[(1/2)\sqrt{x^2 - 4}]
How do you come to the above conclusion by using the quadratic formula?

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The Attempt at a Solution

 
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First convert the equation you're given into a quadratic equation. It'll need to have one term with y^2, one term with just y, and one term that doesn't involve y at all. Can you think of a way to get it into that form? (Hint: multiply both sides of the equation by something)
 
What exactly does "solution" mean?

y\neq 0 so I'm sure you're not looking for the roots of that graph.
 
I presume paridiso meant "solve for y as a function of x". That is what diazona is talking about, certainly.
 
Indeed it is... I hope that's what the OP meant too.
 

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