Hey icelated.
Hint: Multiply both sides by lambda^2 and you should get an equation after re-arranging: a*lambda^4 + b*lambda^2 + c = 0.
Make a substitution u = lambda^2 and solve the quadratic a*u^2 + b*u + c = 0 and then solve for lambda.
The teacher gave us some problems on the board for us to jot down. He said it would prepare us with the final.
Problem:
Optimize the function subject to the constraint
I am not 100% sure what optimize means and if Lagrange multiplier applies but this is what i have so far.
Combining we have:
(1)
(2)
(3)
Solving (1) for x:
(4)
(5)
(6)
Now, add in (4),(5), and (6) for the constraint
then
So, at this point i am stuck. I don't know how to finish.
I don't even know if i was suppose to use Lagrange multiplier or if its correct up to that point?
If someone could let me know if i did the problem correctly and help me finish?
Thank you so much.
Hey icelated.
Hint: Multiply both sides by lambda^2 and you should get an equation after re-arranging: a*lambda^4 + b*lambda^2 + c = 0.
Make a substitution u = lambda^2 and solve the quadratic a*u^2 + b*u + c = 0 and then solve for lambda.
No, gives NOT " "
(6)
Now, add in (4),(5), and (6) for the constraint
then
So, at this point i am stuck. I don't know how to finish.
I don't even know if i was suppose to use Lagrange multiplier or if its correct up to that point?
If someone could let me know if i did the problem correctly and help me finish?
Thank you so much.