MATLAB: I am solving a system of non linear equation using vpasolve but it shows answer as [0*1sym] any other method that I can use

nonlinear equationsvpasolve

The 3 polynomials are mentioned as below. I have to solve for [a1,a2,a3]
P1 =(pi^4*(20000*a1 - 2200))/93750 + 4*pi^2*a1*((10000*(2*pi^2*(a1^2 + 9*a2^2 + 25*a3^2) + 1/8))/((847*pi^2)/1000 + 1/8) - 10000) + (40000*pi^2*a1*(2*pi^2*(a1^2 + 9*a2^2 + 25*a3^2) - (847*pi^2)/1000))/((847*pi^2)/1000 + 1/8)
P2 =(pi^4*(1620000*a2 - 178200))/93750 + 36*pi^2*a2*((10000*(2*pi^2*(a1^2 + 9*a2^2 + 25*a3^2) + 1/8))/((847*pi^2)/1000 + 1/8) - 10000) + (360000*pi^2*a2*(2*pi^2*(a1^2 + 9*a2^2 + 25*a3^2) - (847*pi^2)/1000))/((847*pi^2)/1000 + 1/8)
P3 =(pi^4*(12500000*a3 - 1375000))/93750 + 100*pi^2*a3*((10000*(2*pi^2*(a1^2 + 9*a2^2 + 25*a3^2) + 1/8))/((847*pi^2)/1000 + 1/8) - 10000) + (1000000*pi^2*a3*(2*pi^2*(a1^2 + 9*a2^2 + 25*a3^2) - (847*pi^2)/1000))/((847*pi^2)/1000 + 1/8)

Best Answer

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.
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