Optimize f(x,y,z) = x(adsbygoogle = window.adsbygoogle || []).push({}); ^{3}+ y^{3}+ z^{3}, subject to the constraint g(x,y,z) = x^{2}+ y^{2}+ z^{2}- 1 = 0

Step 1:

I did L = f - [tex]\lambda[/tex]g = x^{3}+ y^{3}+ z^{3}- [tex]\lambda[/tex](x^{2}+ y^{2}+ z^{2}- 1)

Step 2:

I got L_{x}= 3x^{2}- 2[tex]\lambda[/tex]x = 0, L_{y}= 3y^{2}- 2[tex]\lambda[/tex]y = 0, L_{z}= 3z^{2}- 2[tex]\lambda[/tex]z = 0

Now I can't seem to solve these 3 equations to get the critical points & find what [tex]\lambda[/tex] is. Some help please. Thanks.

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# Equation x^2+y^2+z^2=1

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