Problem solving system of nonlinear equations

Hello

I was writing a script where I have 3 equations that I multiply by a constant and that I have to derivate.

After that I add another equation and try to solve that system of four equations to get the result I need, but the answer it gives out doesnt match the real answer (that my teacher gave me)... Here is my script:

syms P1 P2 P3 lambda

I1=510+7.2*P1+0.00142*P1^2;
I2=130+7.85*P2+0.00194*P2^2;
I3=78.0+7.97*P3+0.00482*P3^2;

fc1=1.1;
fc2=1.0;
fc3=1.0;

F1=I1*fc1;
F2=I2*fc2;
F3=I3*fc3;

F1=diff(F1);
F2=diff(F2);
F3=diff(F3);

After I got these three results, based on a tutorial I saw, I did a function:

function F = root2d(x)

F(1) = (71*x(1)^2)/50000 + (36*x(1))/5 - x(4) + 510;
F(2) = (97*x(2)^2)/50000 + (157*x(2))/20 - x(4) + 130;
F(3) = (241*x(3)^2)/50000 + (797*x(3))/100 - x(4) + 78;
F(4)= x(1) + x(2) + x(3) - 850;

end

Finnally I wrote these three lines:

fun = @root2d;
x0 = [0,0,0,0];
x = fsolve(fun,x0)

Unfortunatly the answer it gives out is:

 x =

   1.0e+03 *

    0.2789    0.2966    0.2745    2.6288

I know that the final equations are:

(71*P1^2)/50000 + (36*P1)/5 + 510 = lambda

(97*P2^2)/50000 + (157*P2)/20 + 130 = lambda

(241*P3^2)/50000 + (797*P3)/100 + 78 = lambda

P1 + P2 + P3 = 850

And the real answer is: P1=704.6 P2=111.8 P3=32.6 P4=8.284

What did I do wrong? Is there a better way of doing this?

Answer 1

[Walter Roberson]

There are multiple solutions to those equations, but all the solutions to the equations you give are imaginary.

The values you give as the "real answer" do not work in the equations: if you substitute in those values you give the contradictions [6288.094847 = 8.284, 1031.878526 = 8.284, 342.9445032 = 8.284, 849.0 = 850] and are therefore not solutions.