system of 3 equation with 3 unknown, with two 2nd order equation

Hi,

I am trying to solve a system of 3 equation with 3 unknown, with two 2nd order equation using this code, but unfortunately I don't understand why I do not obtain the result. Thank you in advance

syms QV3 QV2 QVl
eqn1 = 17.79  == QV3 + QV2+QVl;
eqn2 = 0.25*QV3.^2 == 0.14 * QV2^2;
eqn3 = 0.25*QV3.^2 == 3.89* QVl^2;
sol = solve([eqn1, eqn2, eqn3], [QV3 , QV2, QVl])
QV3Sol = sol.QV3
QV2Sol = sol.QV2
QVLsol = sol.QVl

Answer 1

[Star Strider]

The resuillts are strictly numerical (not containing symbolic variables), so use vpasolve instead of solve:

syms QV3 QV2 QVl
eqn1 = 17.79  == QV3 + QV2+QVl;
eqn2 = 0.25*QV3.^2 == 0.14 * QV2^2;
eqn3 = 0.25*QV3.^2 == 3.89* QVl^2;
sol = vpasolve([eqn1, eqn2, eqn3], [QV3 , QV2, QVl])
QV3Sol = sol.QV3
QV2Sol = sol.QV2
QVLsol = sol.QVl

producing:

QV3Sol =
 -214.86507282291207239983881906658
  6.8692131509642582629301134641865
 -30.161934858502498504240076448371
  8.5414023987755051080751389638705
 
QV2Sol =
  287.1255310312749278205504662485
 9.1793721884393279626540627283888
 40.305580843825110030042867255874
 11.413929063852511018159550534661
 
QVLsol =
 -54.470458208362855420711647181924
  1.7414146605964137744158238074247
  7.6463540146773884741972091924965
 -2.1653314626280161262346894985318

These are however still symbolic values. To use them in other calculations, convert them to double-precision values with the double function.

[SYML2nd]

Thank you. Now it works. I don't understand why I can only find numerical result (I am a little bit rusty in math maybe). Why do I have 4 solution for each variable?

[Star Strider]

My pleasure.

It produces strictly numerical results because they are not functions of any other symbolic variables. Any variables would appear in the vpasolve solutions if they existed (and if so, it wouild not be possible to use the double function to convert them to double-precision values).

There are 4 solutions for each variable because each variable is a -order polynomial.