a1 = (-44*Pi^4-1875*P1)*R/(9600*Pi^4*R-1100*Pi^4-75*P3)

a2 = (-1188*Pi^4-625*P2)*R/(19200*Pi^4*R-3300*Pi^4-225*P3)

a3 = R

where

R = roots([2899102924800000000000*Pi^20, -113246208000000000000*Pi^16*((44/3)*Pi^4+P3), 4423680000000000000*((108416/146484375)*Pi^10+(243960584/3515625)*Pi^8+((88/1875)*P1+(594/625)*P2+(814/75)*P3)*Pi^4+P1^2+(1/4)*P2^2+(37/100)*P3^2)*Pi^12, -103680000000000000*((44/3)*Pi^4+P3)*((16153984/10986328125)*Pi^10+(35264208/9765625)*Pi^8+((88/1875)*P1+(396/625)*P2+(44/15)*P3)*Pi^4+P1^2+(1/6)*P2^2+(1/10)*P3^2)*Pi^8, 607500000000000*((44/3)*Pi^4+P3)^2*Pi^4*((30464896/6591796875)*Pi^10-(1931850032/52734375)*Pi^8+((88/1875)*P1+(264/625)*P2+(88/75)*P3)*Pi^4+P1^2+(1/9)*P2^2+(1/25)*P3^2), -86016*(11011*Pi^2-75623375)*Pi^8*(44*Pi^4+3*P3)^3, 11760*Pi^4*(44*Pi^4+3*P3)^4*(121*Pi^2-432125), -(847*Pi^2+125)*(44*Pi^4+3*P3)^5])

... All of the roots. The polynomial is degree 7, so there will be 7 roots, and so 7 solutions to the overall equations.

## Best Answer