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Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=8 and x−y=5.

I found that x = 41/11, y = -14/11, and z = 9/11
Meaning that the max DNE and the min = 178/11
However, my online homework is saying my answer for the min is incorrect. Did I make a mistake on this one?

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