Question

3. Find the minimum value of 2 + y2 + subject to ryc = ?
4. Find​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Let f:R3→R be

f(x,y,z)=x+4z

where

x2+y2+z2≤2.

Find the minimum of f.

This is similar to the question here. However, since this is not an analytic function with complex variable, one may not be able to use the "Maximum modulus principle".

What I think is that one may rewrite the inequality constraint x2+y2+z2≤2 as

x2+y2+z2=2−δδ∈[0,2]

then one can use the "Lagrange Multiplier Method" with the parameter δ. Or one can do it on the xOz plane with the geometric meaning of C in C=x+4z.