Unable to solve symbolic equation> Error Warning: Explicit solution could not be found. > In solve at 81

Hi Pals,

I am not able to find solution to an equation in symbolic Matlab. I would greatly appreciate any help.

syms a1 a2 a3 p c F;
F=sqrt(1-a1*p)+sqrt(1-a2*p)+sqrt((1-a1*p)*(1-a2*p))+c;
Psol = solve(F,p) >> Gives error here

Many Thanks PK

Answer 1

[Walter Roberson]

Two branches of solutions:

(1-RootOf(a2*z^4-2*a2*z^3+(2*a2-2*a1-2*c*a1)*z+a1-c^2*a1-a2,z)^2)/a1

(1-RootOf(a2*z^4+2*a2*z^3+(-2*a2+2*a1-2*c*a1)*z+a1-c^2*a1-a2,z)^2)/a1

Each RootOf(f(z),z) represents the set of values z such that f(z) is 0 -- the roots of the quartics.

The roots of quartics can be represented in closed algebraic form, but they are quite messy.

Answer 2

[Prabhat]

Many thanks for the answer. But please teach me how to do it. I quite didnt get your approach.

Regards pk

Answer 3

[Roger Stafford]

Any solution to your equation must be a root of the following quartic equation in p:

 (a1*a2)^2*p^4-2*a1*a2*(c-1)*(c-3)*p^2+4*(a1+a2)*(c-1)^2*p+(c-1)^3*(c+3) = 0

However, the reverse does not hold. Not all roots of this quartic are necessarily solutions to your equation.