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August 6th, 2017, 04:36 PM  #1 
Senior Member Joined: Nov 2015 From: United States of America Posts: 167 Thanks: 21 Math Focus: Calculus and Physics  Solve feature mathematica
I have been using the Solve feature in mathematica to solve the system of equations for me when using Lagrange Multipliers. It has been a great way to check my work, but now I just began adding another Lagrange multiplier, and now mathematica is not giving me anything for an output. Perhaps I am missing something small here? Solve[{ x^2 + y^2  2 == 0, x + z  1 == 0, Grad[x + y + z, {x, y, z}] == L1 Grad[x^2 + y^2  2, {x, y}] + L2 Grad[x + z  1, {x, z}] }] I also tried Solve[{ x^2 + y^2  2 == 0, x + z  1 == 0, Grad[x + y + z, {x, y, z}] == L1 Grad[x^2 + y^2  2, {x, y,z}] + L2 Grad[x + z  1, {x,y, z}] }] and still no cigar. Any ideas? Huge thanks! Jacob 
August 6th, 2017, 08:27 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,980 Thanks: 1027 
you need to include the multipliers L1 and L2 in the solve for list. Mathematica is pretty picky about wanting the equation list and the solve for list to have the same length. 
August 8th, 2017, 09:04 PM  #3 
Newbie Joined: Aug 2017 From: Vancouver Posts: 1 Thanks: 0  Code: Simplify[{ x^2 + y^2  2 == 0, x + z  1 == 0, Grad[x + y + z, {x, y, z}] == L1 Grad[x^2 + y^2  2, {x, y}] + L2 Grad[x + z  1, {x, z}] }] Code: Reduce[{ x^2 + y^2  2 == 0, x + z  1 == 0, Grad[x + y + z, {x, y, z}] == L1 Grad[x^2 + y^2  2, {x, y, z}] + L2 Grad[x + z  1, {x, y, z}]}, {x, y, z}] Notice that I did include the list of variables for it to find. 

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