Please help me to solve following equations using matlab

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Brajesh Kumar
Brajesh Kumar on 9 Jun 2015
Answered: Alex Sha on 11 Dec 2019
-x(4) + 1-x(1)-x(2)-x(3);
-x(5) + 1-3.*x(1)-7.*x(2);
-x(6) + 4.*x(1)+x(3);
-x(7) + 4*x(1);
-x(8) + 2.*x(3);
-x(9) + 8.*x(1)+12.*x(2)+x(3);
-x(10) + x(3);
-x(11) + 1+1+12*x(1)+4*x(2)+4*x(3);
6.2975e-11 - (((x(6)^4)*(x(8)^8))/((x(4))*(x(5)^3)*(x(11)^8)));
0.0184 - (((x(7)^4)*(x(8)^12))/((x(4))*(x(5)^7)*(x(11)^8)));
4.3202e+16 - (((x(6))*(x(9)^2)*(x(8))*(x(10)))/((x(4))*(x(11)^4)));

Answers (2)

Roger Stafford
Roger Stafford on 9 Jun 2015
For a numerical solution you can use fsolve of the Optimization Toolbox. This requires an initial numerical estimate. It will probably be advisable to substitute the expressions on the right in place of x(4), x(5), ..., x(11), which will leave you just three equations in the three unknowns, x(1), x(2), and x(3), rather than a more difficult eleven equations in eleven unknowns.
For a symbolic solution use 'solve' of the Symbolic Toolbox. I believe this system has as its solution the roots of a polynomial of high order, so the solution would not be explicit but rather expressed in terms of these roots.

Alex Sha
Alex Sha on 11 Dec 2019
change the type of last three equations from (by removing denominator):
6.2975e-11 - (((x(6)^4)*(x(8)^8))/((x(4))*(x(5)^3)*(x(11)^8)));
0.0184 - (((x(7)^4)*(x(8)^12))/((x(4))*(x(5)^7)*(x(11)^8)));
4.3202e+16 - (((x(6))*(x(9)^2)*(x(8))*(x(10)))/((x(4))*(x(11)^4)));
to:
6.2975e-11*((x(4))*(x(5)^3)*(x(11)^8)) - ((x(6)^4)*(x(8)^8));
0.0184*((x(4))*(x(5)^7)*(x(11)^8)) - ((x(7)^4)*(x(8)^12));
4.3202e+16*((x(4))*(x(11)^4)) - ((x(6))*(x(9)^2)*(x(8))*(x(10)));
then the solution could be found easy:
1:
x1: -0.0004228212093028
x2: -0.500690333089145
x3: 0.00195853820342564
x4: 1.49915461609502
x5: 4.50610079525192
x6: 0.000267253366214442
x7: -0.0016912848372112
x8: 0.00391707640685129
x9: -6.00970802854073
x10: 0.00195853820342564
x11: -1.03405451010794E-6
2:
x1: -0.20675122580719
x2: 0.12025367130575
x3: 1.15828260229574E-9
x4: 1.08649755334316
x5: 0.778477978281319
x6: -0.827004902070477
x7: -0.827004903228759
x8: 2.31656524580731E-9
x9: -0.210965749630235
x10: 1.15828263499185E-9
x11: -1.98301461993073E-8

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