anonymous
  • anonymous
Lagrange Multiplier question - How does one solve for their lamba (or even just get the x,y,z etc straight away) when the constraint has higher powers and variables multiplying each other? Example - x^2 + y^2 subject to 17x^2 + 12 xy + 8y^2 = 100 When solving, I end up with a non-linear system, and don't know how to go on.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Let f(x,y)=x^2 + y^2 , and g(x,y)= 17x^2 + 12 xy + 8y^2 - 100 Then df(x,y)+\(\lambda\)dg(x,y)=0 which gives you together with g(x,y)=0 system of 3 equations for 3 unknowns: 2x+\(\lambda\)34x+12y=0 2y+\(\lambda\)12x+16y=0 17x^2 + 12 xy + 8y^2 - 100 =0
anonymous
  • anonymous
3equations and 4unknows^
anonymous
  • anonymous
which is the fourth?

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anonymous
  • anonymous
is the answer lamda = 1/17, -1/18 ? if thats right, i can explain how i got the answer
anonymous
  • anonymous
Thanks, I have that much sorted already though. From there I go to λ = x/(17x+6y) = y/(6x - 8y), and can't get them on their own.
anonymous
  • anonymous
ow oops, sorry myko, my bad... didnt look at that properly
anonymous
  • anonymous
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anonymous
  • anonymous
i hope i did that right^
anonymous
  • anonymous
you didn't take differentials, :)
anonymous
  • anonymous
http://www.bilkent.edu.tr/~sertoz/courses/math114/2011/mid2-sol.pdf page 4, Q3
tkhunny
  • tkhunny
Why is your partial derivative restricted to a singe term. Do the entire expression.
anonymous
  • anonymous
My bad. Should be: 2x+λ (34x+12y)=0 2y+λ (12x+16y)=0 17x^2 + 12 xy + 8y^2 - 100 =0
anonymous
  • anonymous
Thanks guys, I have it now, I was just trying to solve for lambda at the wrong place. I started by getting y in terms of only lambda and x, then then subbing that so I have x in terms of lambda, and then it's simple.

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