How can I isolate "hh" from h(π2R4(H4+H2(H−h)2+(H−h)4))=1h(π2R4(H4+H2(H−h)2+(H−h)4))=1?

Answer 1

I'm assuming you duplicated everything and this is a problem to solve for "h" and not "hh".

Here's how I'm interpreting what you submitted:

h(π²R⁴(H⁴ + H²(H − h)² + (H − h)⁴)) = 1

You would multiply it all out and gather like-terms. If it is supposed to be like I'm showing above, it will turn into a 5th order equation in terms of "h":

k₁h⁵ + k₂h⁴ + k₃h³ + k₄h² + k₅h +k₆

But solving this for h is virtually impossible so I doubt if that is what you are supposed to do.

If I have the correct interpretation above, and if I multiplied it out without making a mistake (not great odds), the coefficients for the "h" terms would be as follows:

k₁ = π²R⁴ (h⁵ term)

k₂ = -4Hπ²R⁴ (h⁴ term)

k₃ = 7H²π²R⁴ (h³ term)

k₄ = -6H³π²R⁴ (h² term)

k₅ = 3H⁴π²R⁴ (h term)

k₆ = -1 (Constant term)