# NSolve/Reduce Help: 3Equations/5Variables

I have this system of equations that I have been trying to solve using Mathematica; I had been running this last evaluation for 30 hours and my computer crashed :/!

So, instead of deciding to run the script again I'd reach out to you guys in case you guys had any ideas on a faster better way to solve this system. Here is my script in its current form:

lm = 1/2;
lm2 = 1/4;
t1 = 0.1031704921564317;
lm2A = lm2*(t2/(t2 + t3));
lm2B = lm2*(t3/(t2 + t3));
r = lm/t1;
r2 = lm/t2;
r3 = lm2/(t2 + t3);
r4 = lm2/t3;
sigmaI = 2.749*10^-4;
sigmaF = 8.719525*10^-6;
h = (sigmaI - sigmaF)/(sigmaI*0.05945062873244056);
r561 = lm2 (t1^2)/3;
r563 = -d (t1*t2) - 2 lm2 (t1*t2) + (lm2 (t2^2)/3);
r564 = d t1 t2 + 2 lm2 t1* t2 - f (t2^2) - (4 lm2 (t2^2)/3) + d t1 t3 + 2 lm2 t1 t3 - f t2 t3 - (7 lm2 t2 t3/6) + (lm2 (t3^2)/6);
eq1 = 1/3 (-3 d (t1^2) + lm2 (-4 (t1^2) - 3 (t2^2) + t2 t3 - 2 (t3^2)) - 3 (f (t2^2) + g (t3^2)));
eq2 = -((lm^2)^2/2 r) - d*t1 - ((lm^2)/(2 r)) + ((lm^2)/(2 r2)) + f*t2 + ((lm2A^2)/(2 r3)) - (((lm2 - lm2A)^2)/(2 r3)) - g*t3 - ((lm2^2)/(2 r4));
eq3 = ((t1^(5/3))/((1 - h*r561)^(4/3))) - ((t2^(5/3))/((1 - h*r563)^(4/3))) + (t3 ((t2 + t3)^(2/3))/((1 - h*r564)^(4/3)));

NSolve[{eq1 == 0.05945062873244056, eq2 == 0, eq3 == 0}, {d, f, g, t2, t3}]


Sorry for the horrendous equations but I had to edit them from mathematica to make them fit here. Again, any help would be greatly appreciated in solving this system! Thank you in advance!

• you can readily eliminate d,f by solving the first two equaitons, leaving just one equation in three unknowns. With that try FindInstance to see if there is any solution – george2079 Jul 25 '16 at 19:48
• You have more unknowns than equations, so it's not clear what NSolve will be able to do even if it does not hang. – Daniel Lichtblau Jul 25 '16 at 23:34

NSolve[{eq1 == 0.05945062873244056, eq2 == 0, eq3 == 0}, {d, f, g, t2, t3}, Reals]