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Homework Help Overview

The problem involves solving the equation y=[(1+y^2)^1.5]/[2(y+sqrt 3)^2] for the variable y. The context suggests a focus on numerical methods and iteration techniques for finding solutions.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants discuss the distinction between numerical and algebraic methods for solving the equation. There is an attempt to clarify what is meant by iteration and how it relates to numerical solutions. Some participants suggest plotting the function to identify roots visually.

Discussion Status

The discussion is ongoing, with participants providing insights into numerical methods and iteration. There is a recognition of the need for further clarification on these concepts, and some participants have shared external resources for additional context.

Contextual Notes

There is a mention of confusion regarding the terminology used in the textbook, particularly the interpretation of numerical solutions versus algebraic methods. Participants are exploring these definitions and their implications for solving the problem.

gimak
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Homework Statement


y=[(1+y^2)^1.5]/[2(y+sqrt 3)^2]; solve for y

Homework Equations


see above

The Attempt at a Solution


I tried to use algebra to solve it, but I can't. The textbook says it can be solved numerically or by iteration. By numberically I think it means algebraically. But I don't know how to do it that way. I don't know what it means by iteration. Can you guys give me an idea of how to do it both ways?
 
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Numerically means using a computer or graphing method to find the answer. Bring the y to the right side so you have f(y)=0. Then plot it to see where f(y) crosses the axis.
Iteration to me also implies a numerical solving method that starts with a guess and moves closer to the zero until you are as close as you need to be.
 
Take the denominator to L.H.S and square both sides. Can you see a pattern?
 
gimak said:

Homework Statement


y=[(1+y^2)^1.5]/[2(y+sqrt 3)^2]; solve for y

Homework Equations


see above

The Attempt at a Solution


I tried to use algebra to solve it, but I can't. The textbook says it can be solved numerically or by iteration. By numberically I think it means algebraically. But I don't know how to do it that way. I don't know what it means by iteration. Can you guys give me an idea of how to do it both ways?

Numerically is NOT algebraically. Rather than trying to explain it I will just give a link to explanations that others have already written out. See
http://mathforum.org/library/drmath/view/61677.html or
http://cfd.mace.manchester.ac.uk/twiki/pub/Main/TimCraftNotes_All_Access/cfd1-numanal.pdf
 

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