Solve a variable in equation

Hi everyone,

I have an equation (function) wich I need solve the lambda value:

f_lambda1 = 101*(1.2-40.40*lambda1).^2 - 200*(1.2-40.40*lambda1)*(1-880*lambda1).^2 - 2*(1.2-40.40*lambda1) + 100*(1-880*lambda1).^4 + 1 == 0;

So I tried to isolate lambda trough the command "x = isolate(f_lambda1, lambda1)" with out success, someone can help me about that solution?

I Thank You

Answer 1

[John D'Errico]

Just use solve. Or vpasolve will also suffice, since this is a polynomial, vpasolve will give all solutions.

lamb = solve(f_lambda1,'maxdegree',4)

Of course, that produces a lengthy, unreadable mess. If you want "the" lambda value, then use vpa on that.

vpa(lamb)
ans =
- 0.00011080430165098438873831754345607 + 0.000010811919008810757147508304534553i
- 0.00011080430165098438873831754345607 - 0.000010811919008810757147508304534553i
  0.0023313621528906538102259208492412 + 0.0000055949768600504265689959078403377i
  0.0023313621528906538102259208492412 - 0.0000055949768600504265689959078403377i

Where we see 4 solutions and only 4. Since your problem is a quartic polynomial in lambda1, those are all the solutions. I have no idea which one you think is correct.