Solving for h: V and tnα, d Given

  • Context: Undergrad 
  • Thread starter Thread starter thomasJDN
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Discussion Overview

The discussion revolves around isolating the variable h from a cubic equation involving parameters V, tnα, d, and h. The focus is on the mathematical manipulation of the equation and the challenges associated with factoring a cubic polynomial.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant requests assistance in isolating h from the equation V = (∏ tnα² h³)/3 + (∏ tnα d h²)/2 + (∏ d² h)/4.
  • Another participant suggests that clarification on the dummy index and limits of multiplication would be helpful.
  • A participant corrects their terminology from "extract" to "isolate" regarding h.
  • It is noted that isolating h involves factoring a cubic equation, which is described as nontrivial.
  • One participant argues that since every term contains h, the non-zero solutions could be the roots of a quadratic, which might be easier to handle.
  • Another participant counters that if V is non-zero, the situation complicates the isolation of h.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the equation and the implications of V being non-zero, indicating that the discussion remains unresolved regarding the best approach to isolate h.

Contextual Notes

The discussion does not clarify the assumptions regarding the values of V, tnα, and d, nor does it specify the limits or definitions related to the dummy index mentioned.

thomasJDN
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hi
can someone help me to extract h from the folowing equetion

V= (∏ tnα² h³)/3 + (∏ tnα d h²)/2 + ( ∏ d² h)/4

thx
 
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Hey thomasJDN and welcome to the forums.

It would help if you said what your dummy index was for the multiplication as well as the limits.
 
im sorry i didnt mean extract
i mean isolate
 
The equation is a cubic in h, so isolating h entails factoring the cubic, which is nontrivial.
 
Mark44 said:
The equation is a cubic in h, so isolating h entails factoring the cubic, which is nontrivial.

yes, but every term contains a h, so the non-zero solutions are the roots of a quadratic, which is somewhat easier.
 
Not if that "V" is non-zero!
 
HallsofIvy said:
Not if that "V" is non-zero!

silly me. you're right of course.
 

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