Help Understanding Transposing Formula in Roarks Formulas for Stress and Strain

[Colnago]

Homework Statement

Hi, I'm looking through Roarks Formulas for Stress and Strain and I am having difficulty following one of the examples. Unfortunately my maths isn't as good as I would like. Hopefully someone can explain to me the steps taken to find the solution.

Homework Equations

The book states the following expression:

4.466^1/n - 2(2.331)^1/n + 1 = 0

From this it finds n = 2.86, unfortunately only the answer is given an no explanation. Can someone help?

Thanks

 

[HallsofIvy]

There is no simple "algebraic" method to combine 4.466^1/n and 2.331^1/n so no simple "algebraic" method to solve that equation. You could do it graphically or using some numerical method such as Newton's method. And "2.86" is only an approximate solution, not exact.

 

[Ray Vickson]

Homework Statement

Hi, I'm looking through Roarks Formulas for Stress and Strain and I am having difficulty following one of the examples. Unfortunately my maths isn't as good as I would like. Hopefully someone can explain to me the steps taken to find the solution.

Homework Equations

The book states the following expression:

4.466^1/n - 2(2.331)^1/n + 1 = 0

From this it finds n = 2.86, unfortunately only the answer is given an no explanation. Can someone help?

Thanks

For the solution of the problem *exactly as it is written*, Maple 14 gets n = 2.822595780, which rounds off to n ≈ 2.82 (NOT 2.86). If we assume, instead, that the equation should really by
$$(67/15)^{1/n} - 2(7/3)^{1/n} + 1=0$$
the solution becomes n = 2.795724837, which rounds off to n ≈ 2.80 (again, NOT 2.86).

Note: Maple uses numerical methods to solve such equations.

 

[SteamKing]

Roark is an old, old text which has several editions. When the equation in the OP was originally solved, the author (or one of his students) might have been using a slide rule or a set of log tables and counting on his fingers and toes.

 

[HallsofIvy]

Hey, don't knock counting on your fingers and toes! I do it all the time.

 

[haruspex]

Hey, don't knock counting on your fingers and toes! I do it all the time.

In binary, I trust?