Solving for h: V and tnα, d Given

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SUMMARY

The discussion focuses on isolating the variable h from the equation V = (∏ tnα² h³)/3 + (∏ tnα d h²)/2 + (∏ d² h)/4. Participants clarify that the equation is cubic in h, making isolation complex. However, it is noted that if V is non-zero, the equation simplifies to finding the roots of a quadratic, which is more manageable. The importance of specifying the dummy index for multiplication and limits is also highlighted as crucial for solving the equation.

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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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