Solving for h: V and tnα, d Given

[thomasJDN]

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

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

thx

 

[chiro]

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.

 

[thomasJDN]

im sorry i didnt mean extract
i mean isolate

 

[Mark44]

The equation is a cubic in h, so isolating h entails factoring the cubic, which is nontrivial.

 

[Deveno]

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.

 

[HallsofIvy]

Not if that "V" is non-zero!

 

[Deveno]

Not if that "V" is non-zero!

silly me. you're right of course.