Solve a system of equations with two unknowns

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Greg
Greg 2012-5-7
评论： Greg Heath 2014-10-1
Hi everyone this should be a pretty easy question. I have two equations with two unknowns
1. -161.20 +2.7Ts -2.7Ta +3.91x10^-8 Ts^4 -5.67x10^-8 Ta^4 =0
2. -78.02 +2.7Ts -2.7Ta -3.57x10^-8 Ts^4 +1.13x10^-7 Ta^4 =0
where Ts and Ta are the unknowns I am trying to calculate. How do I work out the answer for this? Thanks for the help.

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采纳的回答

Greg Heath
Greg Heath 2014-9-25
编辑：Greg Heath 2014-9-30
With an obvious change of variables, the two equations can be combined to obtain
y^4 =( 83.18 + 16.97x^4)/7.48
and
y = x +(117.72 -3.2007x^4)/270
leading to a 16th ? order polynomial equation in x.
Hope this helps.
Thank you for formally accepting my answer
Greg
  1 个评论
Greg Heath
Greg Heath 2014-10-1
Given the two simultaneous equations
y = 0.436 +x -0.011854*x.^4 (1)
y^4 = ( 11.12 + 2.2687*x.^4) (2)
and taking the fourth root of the latter yields
the following 4 equations which can be combined
with the first equation to eliminate y.
y = (+/-)* ( 11.12 + 2.2687*x.^4)^(1/4) (3,4)
y = (+/-)*i*( 11.12 + 2.2687*x.^4)^(1/4) (5,6)
Plotting equations 1,3 and 4
x = -4:0.05:6;
y1 = 0.436 +x -0.011854*x.^4 ; %(1)
y2 = ( 11.12 + 2.2687*x.^4).^(1/4) ; %(2)
y3 = - ( 11.12 + 2.2687*x.^4).^(1/4); %(3)
close all, figure
hold on
plot(x,y1,'k')
plot(x,y2,'b')
plot(x,y3,'r')
Shows that although y2 is always greater than y1,
y3 intersects y1 near x = -3.25 and x = 5.75
All other roots must be complex.
Interesting.
Greg

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更多回答（1 个）

Silibelo Kamwi
Silibelo Kamwi 2012-5-7
Hi Greg, i guess you need to check the optimization toolbox, there is an example of a function dealing with this type of system of nonlinear equations, called fminunc and you might need to get the derivative of your system of equations.
cheers, IK

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