- #1
joemama69
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Homework Statement
Find point closest to origin xy2z3 = 2
Homework Equations
The Attempt at a Solution
note, k = lagrange multiplier
grad f = 2xi + 2yj + 2zk, k grad f = k(y2z3i + 2xyz3j + 3z2xy2k)
k = 2xy-2z-3 = x-1z-3 = (2/3)z-1x-1y-2
y = [tex]\sqrt{2x^2}[/tex]
x = [tex]\sqrt{(y^2)/2}[/tex]
z = [tex]\sqrt{(3y^2)/2}[/tex]
Plug x and z into the original
([tex]\sqrt{(y^2)/2}[/tex])(y2)([tex]\sqrt{(3y^2)/2}[/tex])3 = 2
I tried to simplify that, first i squared both sides
(y2/2)(y4)((27y6)/8) = 4
(27/16)y12 = 4
y = (4(16/27))1/12
y = (64/27)1/12 = 1.074569932
anyone agree, diagree