How to solve for an equation using a series of variables?

Hello!

I'm trying to solve for a variable given a set of equations:

A=By+My^2 
P=B+2y(1+M^2)^0.5
R=A/P
Z=A*R^(2/3)

I want to solve for y (i.e. get an equation in the form of y=)

My knowns are Z, B, and M.

I can calculate y using the excel solver, but I have 50x50 rows and columns so using solver for each cell is not feasible..

Please Help!

Thanks!

Answer 1

[Roger Stafford]

By taking the cube of both sides of the fourth equation and substituting in the expressions for A, P, and R in terms of y, and then rationalizing, you can obtain a tenth-order polynomial equation in y with coefficients in terms of the knowns Z, B, and M. For any given values of these last three quantities you can obtain all ten possible roots using matlab's 'roots' function. Your task then would be to select in each case the value from among the ten possible which one you wish to use. Hopefully many of them will be complex-valued and easy to discard.