Question about solve function




On Sun, 29 Nov 2009, Julien Martin wrote:

< Hello,
< I am trying to solve the following equation with regard to r.
< ***************************************************************************
< 4200=(300*(1/(r+1)^7-1))/(1/(r+1)-1)+4500/(r+1)^7
< solve(%,r);
< [0=13*r^7+90*r^6+266*r^5+434*r^4+420*r^3+238*r^2+70*r-8]
< ***************************************************************************
< What am I missing in order to get the value of r??
< J.
< 
< 

There is no algebraic formula for the roots of a polynomial of degree 5 or more
that is analogous to the quadratic root formula or Cardano's formula. Maxima can
find the roots numerically though,

(%i6) 4200=(300*(1/(r+1)^7-1))/(1/(r+1)-1)+4500/(r+1)^7;

(%o6) 4200 = 300*(1/(r+1)^7-1)/(1/(r+1)-1)+4500/(r+1)^7
(%i7) solve(%,r);

(%o7) [0 = 13*r^7+90*r^6+266*r^5+434*r^4+420*r^3+238*r^2+70*r-8]
(%i8) eq : first(%);

(%o8) 0 = 13*r^7+90*r^6+266*r^5+434*r^4+420*r^3+238*r^2+70*r-8
(%i9) allroots(eq);

(%o9) [r = .08540255121250515,r = .7893408616486308*%i-.3695453097567334,
       r = -.7893408616486308*%i-.3695453097567334,
       r = .9849915622638292*%i-1.224516344611893,
       r = -.9849915622638292*%i-1.224516344611893,
       r = .4384120966613497*%i-1.910178082776088,
       r = -.4384120966613497*%i-1.910178082776088]

Leo

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