# Thread Subject: How to solve

 Subject: How to solve From: parul sotobon Date: 12 Aug, 2010 06:01:33 Message: 1 of 3 Hi all ! I want to solve following nonlinear equation. My variables are c, q and f. I have got values of c but I can not solve for q and f. Can any body suggest me please? a=1000; b=2.5;  s=2;  t=0.5;  hb= 0.5 ; Ab = 5 ;  Av = 10 ;  y=0.5;  w=0.001;  h=0.05;  r=10;  g=5;  tv=3;  l=0.5;  N=3  c=(a*b*(Ab+Av/N)+2*a*b*s+a*b*t)/(a*b-a);  x1=a*c^(-b)*(Ab+Av/N);  x2=y*w+y*w/N+y*h/N;  x3=hb/2+l*w+tv*w+l*h; x2*q^3-x3*q^2-x1=0; f=c*a-q*h ; c, q, t ??? Thanks in advanced Parul
 Subject: How to solve From: Roger Stafford Date: 12 Aug, 2010 06:16:22 Message: 2 of 3 The 'roots' function is your friend. Roger Stafford
 Subject: How to solve From: Walter Roberson Date: 12 Aug, 2010 20:58:13 Message: 3 of 3 parul sotobon wrote: > I want to solve following nonlinear equation. > My variables are c, q and f. > I have got values of c but I can not solve for q and f. > Can any body suggest me please? > > > a=1000; > b=2.5; > s=2; > t=0.5; > hb= 0.5 ; > Ab = 5 ; > Av = 10 ; > y=0.5; > w=0.001; > h=0.05; > r=10; > g=5; > tv=3; > l=0.5; > N=3 > c=(a*b*(Ab+Av/N)+2*a*b*s+a*b*t)/(a*b-a); > x1=a*c^(-b)*(Ab+Av/N); > x2=y*w+y*w/N+y*h/N; > x3=hb/2+l*w+tv*w+l*h; > x2*q^3-x3*q^2-x1=0; > f=c*a-q*h ; > c, q, t ??? Above you want to solve for c, q, and f, but here you ask about c, q, and t. c = 385/18 t = 1/2 Now, let W = RootOf(18*_Z^3-42889*_Z^2-129600000*385^(1/2)*2^(1/2) That is, W are the the three values _Z that satisfy the cubic equation 18 * _Z^3 - 42889 * _Z^2 - 129600000 * sqrt(385) * sqrt(2) = 0 then, f = 192500/9 - 1/1540 * W q = 1 / 77 * W There are analytic solutions for the three routes but they are messy, Their numeric values are approximately, 2416.924245, -17.1010110 + 287.0039229 i, -17.1010110 - 287.0039229 i Note that in deriving these solutions, I assumed that each number given as a decimal (e.g., 0.001) was intended as a compact way to write an exact rational number (e.g., 1/1000), rather than being intended as indicated an approximation (e.g., 95/100000 inclusive to 105/100000 exclusive). Interval arithmetic is much more tiresome.

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